Chapter 6 electromechanics
大学物理-电磁学(英文授课)
大学物理-电磁学（英文授课）IntroductionElectromagnetism is a field of physics that concerns itself with the study of electromagnetic forces and fields. It is a branch of physics that focuses on the interaction between electrically charged particles, including charged particles at rest and moving charges. This course is designed to help students understand the basic principles of electromagnetism, including electric and magnetic fields, electromagnetic radiation, and electromagnetic waves.Electric FieldsElectric fields are created by electric charges, which are either positive or negative. The electric field is said to be the space surrounding a charged particle. If another charged particle is placed in the electric field, it will experience a force. The direction of the force depends on the charge of the particle and the direction of the electric field.Magnetic FieldsMagnetic fields are created by moving charges. A magnetic field is said to be the space surrounding a magnetic object. If a charged particle is placed in a magnetic field, it will move in a circular path. The direction of the circular path depends on the charge of the particle and the direction of the magnetic field. Electromagnetic FieldsAn electromagnetic field is created by the interaction of an electric field and a magnetic field. Electromagnetic fields have both electric and magnetic components, and they travel through space at the speed of light. Electromagnetic waves are a form of electromagnetic radiation that carries energy. Electromagnetic radiation includes radio waves, microwaves, infrared light, visible light, ultraviolet light, X-rays, and gamma rays.Maxwell's EquationsMaxwell's equations describe the behavior of electric and magnetic fields. They are a set of partial differential equations that relate the electric and magnetic fields to the electric charges and currents that are present. The equations describe how an electric field can produce a magnetic field, and a magnetic field can produce an electric field. They also describe how the electromagnetic fields propagate through space.Electromagnetic WavesElectromagnetic waves are waves of energy that are propagated through space by the interaction of electric and magnetic fields. Electromagnetic waves do not require any medium to propagate through. They can travel through a vacuum, which is why they are also known as vacuum waves.Electromagnetic waves are classified based on their frequency and wavelength. Radio waves have the lowest frequency, and gamma rays have the highest frequency. Radio waves have the longest wavelength, and gamma rays have the shortest wavelength.Applications of ElectromagnetismElectromagnetism has many practical applications in our daily lives. Some of the most common applications include electric motors, generators, transformers, telecommunication devices, medical imaging devices, and microwave ovens. Electromagnetism has also played a significant role in the development of modern technology, including computers, television, radio, and mobile phones.ConclusionElectromagnetism is a fascinating field of physics that has wide-ranging applications in our daily lives. This course provides students with a comprehensive understanding of electric and magnetic fields, electromagnetic radiation, and electromagnetic waves. By studying electromagnetism, students can gain a deeper appreciation for the fundamental principles that govern the behavior of the universe around us.Electromagnetism is one of the four fundamental forces of nature, along with gravity, strong nuclear force, and weak nuclear force. It is a field of physics with numerous applications in our modern society. Without the understanding of electromagnetism, we would not have the modern comforts that we have today, including electricity, the internet, cell phones, and many other devices.One of the most significant contributions of electromagnetism to modern society is the use of electric motors. Electric motors are devices that convert electrical energy into mechanical energy.They are used in a wide range of applications, from household appliances to transportation systems. The underlying principle of electric motors is electromagnetic induction, which is the process of inducing an electric current in a conductor by varying the magnetic field around it.Another important application of electromagnetism is in generators. Generators are devices that convert mechanical energy into electrical energy. They are often used in power plants to generate electricity that is distributed to homes and businesses. The principle of electromagnetic induction is also used in generators. When a conductor moves through a magnetic field, an electric current is induced in the conductor.Electromagnetism also plays a central role in the functioning of transformers. A transformer is a device that changes the voltage of an alternating current (AC) power supply. Transformers are used to step up or step down the voltage of an AC power supply. They are used in power grids to maintain a constant voltage throughout the grid. The principle used in transformers is electromagnetic induction, with the primary and secondary coils of wire interacting with the magnetic field to produce the desired voltage change. Telecommunication devices, including radios, televisions, and cell phones, also rely on the principles of electromagnetism. The radio waves used for communication are a form of electromagnetic radiation. Radio waves are used to transmit and receive signals between devices. The workings of these devices depend on the principles of electromagnetic induction and electromagnetic radiation.In addition to powering devices, electromagnetism is used in medical imaging devices. Magnetic resonance imaging (MRI) machines use magnetic fields and radio waves to produce images of the body's internal structures. The patient is placed in a powerful magnetic field, which causes the protons in their body to align with the field. A radio wave is then sent through the body, causing the protons to produce a signal. The signal is detected, and an image is produced based on the strength and location of the signal.Microwave ovens are another example of electromagnetism in action. These appliances use microwaves to cook food. Microwaves are a type of electromagnetic radiation with a frequency of around 2.4 GHz. The microwaves cause the water molecules in the food to vibrate rapidly, producing heat. This heats the food quickly and evenly, making it a popular method for cooking.The study of electromagnetism has also led to the development of modern technology. Computers, televisions, radios, and cell phones all rely on the principles of electromagnetism. The development of these technologies has revolutionized the way we live and communicate. The internet, for example, would not exist without the principles of electromagnetism.In conclusion, electromagnetism is a fascinating field of physics with numerous practical applications in our daily lives. It is the foundation of modern technology, and our society would not be the same without it. By studying electromagnetism, we can gain a deeper understanding of the world around us and appreciate thefundamental principles that govern our universe. As technology advances, we can expect even more exciting and innovative applications of electromagnetism in the years to come.。
半导体物理器件与工艺英文原版
半导体物理器件与工艺英文原版Semiconductor Physics, Devices, and Fabrication.Introduction.Semiconductors are materials with electricalconductivity between that of conductors and insulators.This unique property makes them essential for a wide rangeof electronic devices, including transistors, diodes, and solar cells.Semiconductor Physics.The electrical properties of semiconductors are determined by their electronic band structure. In an insulator, the valence band (the band of electrons that are tightly bound to the atoms) is filled, and the conduction band (the band of electrons that are free to move) is empty. In a conductor, the conduction band is partially filled. In a semiconductor, the conduction band is empty and thevalence band is filled, but there is a small energy gap between the two bands.When a semiconductor is exposed to light or heat, electrons can be excited from the valence band to the conduction band. These electrons are then free to move, and the semiconductor becomes more conductive. This phenomenon is known as intrinsic conduction.Semiconductors can also be doped with impurities to increase their conductivity. Donor impurities add electrons to the semiconductor, while acceptor impurities remove electrons. Doped semiconductors are used to create transistors, diodes, and other electronic devices.Semiconductor Devices.Transistors are the basic building blocks of electronic circuits. They can be used to amplify signals, switch currents, and store data. Transistors are made from three layers of semiconductor material: the emitter, the base, and the collector.Diodes are another important type of semiconductor device. They allow current to flow in one direction but not the other. Diodes are used in a variety of applications, including rectifying AC currents and protecting circuits from overvoltage.Solar cells are semiconductor devices that convertlight into electricity. Solar cells are made from photovoltaic materials, which are materials that generate an electrical current when exposed to light. Solar cells are used to power a variety of devices, including calculators, watches, and satellites.Semiconductor Fabrication.Semiconductors are fabricated using a variety of processes, including lithography, etching, and deposition.Lithography is the process of creating patterns in semiconductor materials. Lithography is used to create the features of transistors, diodes, and other electronicdevices.Etching is the process of removing material from semiconductor wafers. Etching is used to create the trenches and vias that connect the different layers of a semiconductor device.Deposition is the process of adding material to semiconductor wafers. Deposition is used to create the metal layers that connect the different parts of a semiconductor device.Semiconductor fabrication is a complex and precise process. The quality of the final product depends on the accuracy of each step in the fabrication process.Conclusion.Semiconductors are essential for a wide range of electronic devices. The physics of semiconductors and the processes used to fabricate semiconductor devices are complex and challenging, but they are also essential forthe development of new and innovative electronic technologies.。
kinetics 1
• Average speed is defined as total distance divided by the time interval
s distance time interval
•Instantaneous velocity
x dx v lim t 0 t dt
The instantaneous velocity equals the derivative of x with respect to t
Derived quantities and derived units （导出量和导出单位）
speed :
density:
s v t m V
m/s
kg/m3
Dimension (量纲)
[v ] [ s]/[t ] LT
1 3
[ ] [m]/[V ] ML
Chapter 2: Kinematics 1
What is Physics ?
Physics is the discipline of science most directly concerned with the fundamental law of nature.
Physics deals with basic components of matter, motion and their interaction.
Velocity and speed • Average velocity is defined as the ratio of the displacement of the particle to the time interval.
x2 x1 x displacement v t2 t1 t tr 1 : Measurement
激光原理课件chapter6
Absorption cross section of Nd3+ in YAG (solid line) and Cr3+ (chromium, 铬) in alexandrite (紫翠玉， BeAl2O4, dashed line)
4
Principles and Technologies of lasers
material (absorption efficiency) f pq : raction of absorbed power or energy actually used to populate the upper laser level (power or energy quantum efficiency)
(6.2.4)
7
Principles and Technologies of lasers
C,
p r t a pq
(6.2.5)
r : efficiency of conversion from electrical input to the lamp to light output
9
Principles and Technologies of lasers
Chapter 6 Pumping Processes
FIG. 6.8. Absorption coefficient versus wavelength in the wavelength range of interest for diode laser pumping: (a) Nd:YAG (solid line) and Nd:glass (dashed line). Neodymium concentration is 1.52 x 10^20cm^3 for Nd:YAG (1.1 atomic % doping) and 3.2 x 10^20cm^-3 for Nd:glass (3.8% by weight of Nd2O3). (b) Yb:YAG (solid line) and Yb:glass (dashed line); ytterbium concentration is 8.98 x 10^20cm^-3 for Yb:YAG (6.5 atomic %) and 1 x 10^21cm^-3 for Yb:glass.
电化学原理_(李狄_著)北航出版社_课后1-7章习题参考答案
电化学原理第一章习题答案1、解：2266KCl KCl H O H O 0.001141.31.010142.31010001000c K K K K cm 11λ−−−−×=+=+=+×=×Ω溶液 2、解：E V Fi i =λ，FE V i i λ=，，， 10288.0−⋅=+s cm V H 10050.0−⋅=+s cm V K 10051.0−⋅=−s cm V Cl 3、解：,62.550121,,,,2−−⋅Ω=−+=eq cm KCl o HCl o KOH o O H o λλλλ2O c c c ,c 1.004H H +−====设故，2,811c5.510cm 1000o H O λκ−−−==×Ω4、（1）121,,Cl ,t t 1,t 76.33mol (KCl o KCl o Cl cm λλλλλ−−−−+−+−=++=∴==Ω⋅∵中）121121121,K ,Na ,Cl 73.49mol 50.14mol 76.31mol (NaCl o o o cm cm cm λλλ++−−−−−−−=Ω⋅=Ω⋅=Ω⋅同理：，，中）（2）由上述结果可知： 121Cl ,Na ,121Cl ,K ,mol 45.126mol 82.142−−−−⋅Ω=+⋅Ω=+−+−+cm cm o o o o λλλλ，在KCl 与NaCl 溶液中−Cl ,o λ相等，所以证明离子独立移动定律的正确性；（3） vs cm vs cm u vs cm u F u a o o l o l o i o /1020.5,/1062.7,/1091.7,/24N ,24K ,24C ,C ,,−−−×=×=×==++−−λλ5、解：Cu(OH)2== Cu 2++2OH -,设=y ；2Cu c +OH c −=2y 则K S =4y 3因为u=Σu i =KH 2O+10-3[y λCu 2++2y λOH -]以o λ代替λ（稀溶液）代入上式，求得y=1.36×10-4mol/dm 3所以Ks=4y 3=1.006×10-11 (mol/dm 3)36、解： ==+，令=y ，3AgIO +Ag −3IO Ag c +3IO c −=y ，则=y S K 2，K=i K ∑=+（y O H K 2310−+Ag λ+y −3IO λ）作为无限稀溶液处理，用0λ代替，=+y O H K 2310−3AgIO λ则：y=43651074.1104.68101.11030.1−−−×=××−×L mol /;∴= y S K 2=3.03810−×2)/(L mol 7、解：HAc o ,λ=HCl o ,λ+NaAc o ,λ-NaCl o ,λ=390.7，121−−⋅Ωeq cm HAc o ,λ=9.02121−−⋅Ωeq cm ∴α0/λλ==0.023，==1.69αK _2)1/(V αα−510−×8、解：由欧姆定律IR=iS KS l ⋅=K il,∵K=1000c λ,∴IR=1000il cλ⋅=V 79.05.0126101010533≈××××− 9、解：公式log ±γ=-0.5115||||+Z −Z I （设25）C °（1）±γ=0.9740，I=212i i z m ∑,I=212i i c z ∑，=（）±m ++νm −−νm ν1（2）±γ=0.9101，（3）±γ=0.6487，（4）±γ=0.811410、解：=+H a ±γ+H m ，pH=-log =-log （0.209+H a 4.0×）=1.08电化学原理第二章习题答案1、 解：()+2326623Sb O H e Sb H O ++++ ，()−236H H +6e + ，电池:2322323Sb O H Sb H O ++解法一：00G E nF ∆=−83646F =0.0143V ≈，E=+0E 2.36RT F 2232323log H Sb O Sb H OP a a a ==0.0143V0E 解法二：0602.3 2.3log log 6Sb Sb H H RT RT a a F Fϕϕϕ+++=+=+； 2.3log H RTa Fϕ+−=∴000.0143Sb E E ϕϕϕ+−=−===V2解：⑴，(()+22442H O e H O +++ )−224H H +4e + ；电池:22222H O H O +2220022.3log 4H O H O P P RT E E E Fa =+= 查表：0ϕ+=1.229V ，0ϕ−=0.000V ，001.229E V ϕϕ+−∴=−= ⑵视为无限稀释溶液，以浓度代替活度计算()242Sn Sn e ++−+ ，()，电池:32222Fe e Fe ++++ 23422Sn Fe Sn Fe 2+++++ +23422022.3log 2Sn Fe Sn Fe C C RT E E F C C ++++=+=（0.771-0.15）+220.05910.001(0.01)log 20.01(0.001)××=0.6505V ⑶()，，(0.1)Ag Ag m e +−+ ()(1)Ag m e Ag +++ (1)(0.1)Ag m Ag m ++→电池：(1)0(0.1)2.3log Ag m Ag m a RT E E F a ++=+，（其中，=0） 0E 查表：1m 中3AgNO 0.4V γ±=，0.1m 中3AgNO 0.72V γ±=， 2.310.4log0.0440.10.72RT E V F×∴==× 3、 解：2222|(),()|(),Cl Hg Hg Cl s KCl m Cl P Pt ()2222Hg Cl Hg Cl e −−++ ，()222Cl e Cl −++ ，222Hg Cl Hg Cl 2+ 电池：222200002.3log 2Cl Hg Hg Cl P a RT E E E F a ϕϕ+−=+==−∵O 1.35950.2681 1.0914(25C)E V ，∴=−=设 由于E 与无关，故两种溶液中的电动势均为上值Cl a −其他解法：①E ϕϕ+=−−0，亦得出0E ϕϕ+=−−②按Cl a −计算ϕ+，查表得ϕ甘汞，则E ϕϕ+=−甘汞 4、 ⑴解法一：23,(1)|(1)()H Pt H atm HCl a AgNO m Ag +=()222H H e +−+ 222，()Ag e Ag +++ g ，2222H Ag H A ++++ 电池：有E ϕϕϕ+−=−=+，02.3log()AgAgAg RTE m Fϕγ++±∴=−。
中文版ExploringChemistrywithElectronicStructureMethos
中文版Ｅｘplｏring-Chemisｔry-ｗiｔh－Electronｉｃ-Structuｒｅ-Mｅｔhos－————————————————————————————————作者：————————————————————————————————日期:Expｌoring Chｅmｉstry with EleｃtroｎiｃStruｃture ＭｅｔｈｏdSecｏｎd EｄithionJaｍeｓB．FｏｒｅｓｍanAｅleenＦｒischGaussｉａｎ,IncPittｓburgh,ＰA2002年９月25日特别声明本文转自南开大学BＢS网站,在此对译者表示衷心感谢!!!！用Gａusｓian研究化学问题说明接触Gaｕssian已经很久了,但真正用Ｇaussｉan做东西还是临近博士毕业时的事情。
当时做计算的时候,就特别希望有一本具体怎么使用从头算的书，可惜一直没有找到。
来到这里后,在新买的Gauｓsｉan９8包中发现了这本书，感觉如获至宝，也希望能够提供给想用Gaus ｓｉan做东西的朋友。
我不是专门做量化的，很多术语不清楚怎么翻译,手头又没有中文的资料,错误的地方，只能希望内行来指点了。
其实这本书里面介绍的东西,不止限于Ｇaｕssian程序的。
对于从事从头算研究的都有帮助。
内容中有很多计算实例,都是在Gauｓsｉａｎ94,98程序中提供的。
节译自Eｘploｒing CheｍｉstrｙｗitｈElecｔroｎiｃStｒｕctuｒe Meｔhoｓ，SeconｄEditｉｏn,作者JａmeｓＢ。
Ｆoｒeｓmａｎ,ElｅｅｎＦrisｃh出版社Gaｕｓsiａn,Iｎc,ＵSA,1９96目录特别声明ﻩ错误!未定义书签。
用Gaｕｓsiａｎ研究化学问题........................................................................ 错误!未定义书签。
说明ﻩ错误!未定义书签。
第七章 电化学(第六版)
或
M ( 还 原 态 ) M ( 氧 化 态 )z e
：
通过电极的电量正比于电极反应的反应进度与电极反应电
荷数的乘积，比例系数为法拉第常数。
Q zF
Q 通过电极的电量
z 电极反应的电荷数(即转移电子数), 取正值。
电极反应的反应进度， = nB/B F 法拉第常数; F = Le = 96485.309 C/mol
13
第十三页，编辑于星期五：十七点 四十九分。
定义:离子迁移数为离子B所运载的电流占总电流的分数
（ 以t 表示，其量纲为一）
若溶液中只有一种阳离子和一种阴离子，它们的迁移数分别以
t+和t 表示，有:
t
I II
t
I II
（1 ）
显然 t t 1
对于含有多种离子的电解质溶液则有：
tB 1
14
第十四页，编辑于星期五：十七点 四十九分。
2
第二页，编辑于星期五：十七点 四十九分。
物理化学中的电化学主要着重介绍电化学的基础理论部 分 用热力学的方法来研究化学能与电能之间相互转换的规律 ，重点是原电池和电解池工作原理与热力学性质，分为以下两个
部分：
1. 利用化学反应来产生电能将能够自发进行的化学反
应放在原电池装置中使化学能转化为电能；
应可进行。
H2
O2
极板/溶液：电子得失
溶液中： 离子定向迁移
利用电能以发生化学反应 的装置成为电解池
电解池
5
第五页，编辑于星期五：十七点 四十九分。
例：氢与氧的反应
电解池：
阴极: 2H+ + 2e－ H2
阳极： H2O12O2+2H++2e-
电动力学导论格里菲斯中文版第五章
电动力学是物理学中非常重要的分支之一，它研究电荷和电荷所产生的电场之间的相互作用。
而《电动力学导论格里菲斯中文版》是由美国加州大学河滨分校的大卫·J·格里菲斯所撰写的一本电动力学经典教材，其中第五章主要讨论的是磁场的静止情况和运动情况。
1. 静磁场第五章开篇即介绍了静磁场的基本概念和性质。
在这一部分中，格里菲斯首先介绍了磁场的产生原理，即电流产生磁场的安培定律。
通过对安培定律的深入探讨，读者可以逐步理解磁场的强弱和方向是如何受电流产生的影响的。
在阐述完安培定律后，格里菲斯进一步引入了磁场的高斯定律和比奥-萨伐特定律，这两个定律分别用于描述磁场的闭合性和洛伦兹力的作用。
2. 磁场的变化第五章的第二部分涉及到磁场的变化情况。
讨论了磁感应线圈、法拉第电磁感应定律和自感等内容。
这部分内容探讨了磁场与时间的关系，解释了磁场变化对于感生电动势和感生电流的影响，为后续章节的讨论奠定了基础。
3. 资料分析和补充第五章的第三部分主要是对前两部分内容的回顾和总结。
并结合实际例子来对磁场的理论知识进行应用和延伸，使读者能够更加直观生动地理解磁场的作用和应用。
总结通过对《电动力学导论格里菲斯中文版》第五章的深入阐述和梳理，不仅加深了我对静磁场和磁场变化的理解，同时也为我在电动力学领域的学习和研究提供了丰富的知识储备。
在学习过程中，我也意识到电动力学作为物理学中的重要分支，其理论知识和实际应用都具有广泛的价值和意义。
希望通过对电动力学的学习和探索，能够在相关领域取得更多的成果，并为科学研究和技术创新做出自己的贡献。
第五章的内容涵盖了静磁场和磁场的变化，这些内容是电动力学中非常重要的组成部分。
在这一部分中，格里菲斯详细地介绍了静磁场的基本概念和性质，包括安培定律、高斯定律和比奥-萨伐特定律。
通过对这些定律的深入探讨，读者可以更加深入地理解磁场与电流之间的关系，以及磁场的闭合性和洛伦兹力的作用。
在第二部分中，磁场的变化成为焦点，涉及到磁感应线圈、法拉第电磁感应定律和自感等内容。
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Stress
Normal Stress = Force per unit Area
Shear Stress
Shear Modulus
Strain
Strain (εx, εy, εz) is normalized deformation (length change per unit length) – Dimensionless
Euler-Bernoulli beam equation
Cantilever beam w/t point load at the free end
M( x ) F ( L x ) d 2y F( L x ) 2 d x EI
I of interest in MEMS
I x y 2 dA
Squeeze Film Damping Model Slide fileze film damping can be large and affect the dynamics and noise floor of sensors; it can be reduced by vacuum packaging or damping holes. However, vacuum packaging can significantly increase the cost and manufacturing complexity and any leakage in the vacuum package will be a source of longterm drift in the sensor.
The normal stress is easy to calculate. It can be determined by the relationship:
Small slope
Bigger slope
6.2 DAMPING MODELS
There are two frequently encountered configurations of moving MEMS surfaces interacting with a viscous gas flow that produce energy dissipation, which give rise to damping
Interested : the deflection of the endpoint of the beam, which is:
which gives us two spring constants
Types of load
Static equilibrium
Beam and reaction forces
A
I y x 2 dA
A
Other beams commonly used in MEMS
Torsion
What is Torsion?
Ip of interest in MEMS
I 2dAI x I y
A
Oscillatory Motion of beam
Structural beams are often operated in resonant modes analyze the oscillatory motion of beams. Resonant frequency1 is determined by the equation:
Chapter 6 Electromechanics
This chapter will present an overview of the important topics in structural mechanics, damping, and electrical circuit elements. The objective of this presentation of electromechanics is to provide the basis for analysis of actuator and sensor systems, which frequently involve a coupling of the mechanics of a structure (i.e., cantilver, seismic mass, flexural supports) and an electrical system that senses the motion or provides a force for actuation.
dx ds d cos
the strain as a function of position along the beam is
the stress and strain are related by the Young’s modulus,
Integrating over the cross-section of the beam :
Failure of Structural Beams
A structural beam will fail when the maximum allowable stress has been exceeded. The stresses in materials should not approach either yield or ultimate stress. There are several methods useful for calculating stresses in materials.
Under an external load, the beam is in static equilibrium with reaction forces (and bending moments). Summing moments about point B, we can get reaction forces.
Beam Bending
define a coordinate system on the undeformed beam where x is the distance along the length of the beam and z is the vertical distance above the neutral axis of the beam. If we take the thickness of the beam to be a, then we see that z varies from -a/2 to a/2.
usually written:
where is ρ the radius of curvature, M is the moment.
Calculate the shape of a cantilevered beam with a pure moment applied at the free end of the beam.
6.1 STRUCTURAL MECHANICS In this parts, we will introduce some concept Of the Cantilever beam analysing.
Elasticity Basic definitions
Stress σ Strain ε Young’s Module E Possion Ratio v Moment of inertia I
MEMS devices invariably involve engineering of multiphysics designs to attain a design objective. The two physical domains most frequently utilized in MEMS devices are : structural dynamics electrical dynamics
The cantilevered beam implies a boundary condition of:
ODE:
integrate the ODE directly,
Subsituting the boundary conditions shows that the constants of integration are zero
For isotropic elastic materials, stress and strain satisfy Hook’s Law
E is called Young’s modulus. Dimension of E is Pa (same as stress)
Poisson Ratio
For example, a MEMS accelerometer requires the suspended seismic mass to have a preferred mode of vibration in the sensitive axis at a specific resonant frequency. This device would also have an electrical sense interface to transduce the motion of the seismic mass and, possibly, electrical force feedback to maintain the position of the accelerometer sense mass at a neutral position. The damping of the accelerometer seismic mass will greatly influence the dynamics of the system and needs to be considered in the design.