大学英文物理实验报告(简易)

“Simple Harmonic Motion Experiment”

Abstract

In this lab we are using spring weights, rod, clamp, string force sensor and rule to determine the spring constant using two different methods.

Experiment Description

Before starting the experiment, we need to calculate the spring constant k by using:

F = -kx

Which F is force that pull or push the force sensor, x is displacement while weights are hanging on the spring. If the spring we use obey Hooke’s law, displacement(x) will follow the equation:

x = A cos(ωt+Φ) (1)

While A is the amplitude of oscillation,ω is the angular frequency in rad/s, Φ is the staring angle and t reference time in second. For both Φ and ω, we can use the following equations:

ω = (k/m)^(1/2) (2)

T = 2π[(m/k)^(1/2)] (3)

For the first part of the experiment, we hang a mass holder from the end of the spring and measure the displacement from this point. Starting to add masses on the hanger from mass = 0.15kg. Measure the length changing and add additional 0.1kg at the end of the spring. Repeat 6 times and record the data to a excel table.

For the second part, set up the computer and Data studio, open a graph reference force vs time. Set rate to 50Hz. Bump the weight in order to fit the graph like a sine wave, using fit area to find the period T. Repeat adding mass on the spring by 0.1kg each time. By squaring both side of (3), we have:

T^2 = (4π^2)m/k

Plot T^2 versus m to a excel form. Using linear equation to determine the slope k.

Experiment Result

Part 1，Force vs. Displacement

Part 2, T^2 vs. Mass

2.Value k found in Part 2: 29.0

3.

3.Percentage difference: 0.24%.

4.While y axis, which T^2 is 0, Mass actually is not 0. Because spring has mass on it and

will affect the total mass. Also, Air resistance will also being a fact.

5.While on the moon, mass will also about 1/6 like on Earth. so the displacement will

shorter. Because of no air resistance acting on the experiment, Part 2 may become more accurately.

Conclusion

The experiment tell me about the constant resilience of a object. The force acts on this object will appears shape changes, which will follow F=-kx. By using two different ways to evaluate the constant k of the spring, we also know that we c an’t over extend object because there is a limit. While in the limitation, force and displacement will follow the Hooke’s law. After the force exceed over the limit, rule will break.