# Physics 120/130

## Simple Harmonic Motion

From this general outline, please investigate the following using methods you have learned about in previous labs and write up a full report being careful to explain yourself fully.

### Apparatus

Spring, weight hanger, set of masses, digital balance, meter stick, stopwatch, and sonic ranger.

### Outline

You will investigate the following items using the techniques and methods learned in previous labs and write a full lab report, including the procedure you developed and used.

1. By hanging known weights from the spring, determine k. Is the plot linear? Do you expect it to be?  This method should be independent of the method used in part 5.

2. Measure the periods of oscillation for different initial amplitudes and determine whether T depends on A. This determination should be quantitative (meaning a number that can definitively state what this dependence is).

3. Experimentally determine (with graphs) how the position, velocity, and acceleration of a mass on a spring depend on time. Note: this is not the same thing as part 2. Do these graphs represent the motion in the ways you expect?

4. Experimentally determine (with a graph) how the amplitude of a mass on a spring depends on time. Note: this is not the same thing as part 2 or part 3.

5. Since the mass we use and the spring are both hanging and subject to gravity, we may have to consider gravity's effect. It turns out that we can "ignore" gravity acting on the hanging mass. Why? If the mass of the spring is negligibly small compared to the mass attached to the spring, then the period is given by . To account for the effect of the mass of the spring, however, we need to add the spring's mass into the formula for the period, , where ms is the mass of the spring and a is a constant, not an angular acceleration.  Measure the period of oscillation for different masses m. What are the units of a? Determine k and a from your measurements. This method should be independent of the method used in part 1. You should also make sure to report a and k properly.

You have access to: a spring, weight hanger, set of masses, digital balance, meter stick, stopwatch, note cards, photogate, and sonic ranger.