Question

A simple pendulum is a mass on a string. Does the period with which the pendulum swings depend on mass, length, initial angle, or some combination of those? In this lab, you will vary each of these three parameters independently and measure the affect they have on period. Using graphical analysis techniques, you will determine the functional dependence of period on each of those quantities.

Not knowing how any of these quantities—length l, mass m, and initial angle (theta)—affect the period T of a pendulum, we’ll start with the assumption that they are related by the very generic equation

T = A*l^a*m^b*(theta)^c

Where A, a, b and c are constants. This type of relation is known as a power function and can be linearized by taking the natural logarithm of both sides of the equation. This allows you to isolate the individual fitting parameters.

1.)

If you vary the pendulum length, l, while holding the mass and initial angle constant, how could you find the value of the exponent, a, from a graph of ln(T) vs ln(l)?

2.)

If period is not dependent on one of the variables listed above (length, mass, initial angle), what should the value of that exponent be?

3.)

Look up the equation for the period of a simple pendulum from a dependable source. What variables should period depend on?

4.)

Using the relation, you just looked up for the period T of a pendulum, what should the values of A, a, b and c be in the equation above? What should the units of A be?

Answer 1