Spring Motion, Part 2

Spring Motion

Part 2: The Damped Spring

If you are gathering your own data, add a damping effect to the motion as shown in the figure at the right, using a piece of cardboard (or other light, rigid material) to create air resistance. Run the experiment in the same manner as before.

If you do not have a facility for data gathering, you may use ours instead.

Here we consider the more complicated initial value problem

with y(0) = y₀ and y'(0) = 0. The worksheet is set up to define a model function for this motion. We know from previous work that this model function y = y(t) has the form

Since we do not know the damping constant c, we cannot evaluate the constants R, L, theta, and delta directly. You will have to experiment to find appropriate values; i.e., try values and then compare the graph of y(t) with the plot of the data.

Plot the data, yours or ours, and estimate R from the data.
Next adjust theta (with delta = 0) so that the oscillations have about the correct frequency.
Change L to obtain appropriate damping.
Now adjust delta.
After "tweaking" the values for the best fit, record your values of R, L, theta, and delta.
Describe how good the approximation is.
Find a formula for L in terms of c and m.
Use your experimental value of L and your known value of m to estimate the value of c in the differential equation.

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