Hooke's Law and Simple Harmonic Motion

1. Measure the spring constant and potential energy of a spring and confirm the relationship between the mass and oscillatory period T.

1. Obtain a spring with a known spring constant, a stand to attach the spring to, at least 5 weights of varying masses that can be attached to the spring, a meter stick, and a stopwatch.
2. Secure the stand to a solid foundation and attach the spring to the stand. Make sure that there is enough room below the spring for it to stretch without hitting the table or ground.
3. For each of the masses, calculate the force exerted on the spring by the Earth's gravitational force (F = mg). Start with the least-massive weight. Record these values in Table 1.
4. Measure how high above the surface of the table the spring is while in its un-stretched position.
5. Attach the least-massive weight to the spring and measure the displacement Δy1 (see Figure 1). Record this displacement in Table 1.
6. With the weight attached, slightly raise the weight before releasing it. Observe the oscillatory motion. Measure the period T with a stopwatch. For a more accurate measurement, record the time for multiple periods and divide that time by the number of periods observed. Do this multiple times and record the average time measured for the period T in Table 1.
7. Repeat steps 1.5-1.6 for all of the masses, in order of increasing mass.
8. Calculate the potential energy of the spring for each of the different masses and record them in Table 1.
9. Plot the force F as a function of displacement Δy. According to Equation 1, this should be linear. Fit a slope to the line. This slope will correspond to the spring constant k. Compare the measured value to the known value of the spring.
10. Using the known spring constant and Equation 5, calculate what the period T of oscillation should be for each of the masses; report them in Table 1. Compare them to the T that was measured with a stopwatch in step 1.6.

Figure 1: Srping oscillation,