Question

An astronaut lands on an alien planet. He places a pendulum (L = 0.300 m) on the surface and sets it in simple harmonic motion, as shown in this graph.


Answer the following questions:
a. What is the period and frequency of the pendulum’s motion?
b. How many seconds out of phase with the displacements shown would graphs of the velocity and acceleration be?
c. What is the acceleration due to gravity on the surface of the planet in m/s2? Determine the number of g-forces.

Answer 1

here are the graphs

Answer 2

Get the period by seeing how long between peaks (or troughs).
I counted 4 troughs over 3 s, making the time between them T = (3/4)s. The frequency is 1/T, 1/period.

The curve is a sine wave, 0.05 sin(2 pi t / T) = 0.05 sin(2 pi f t)

The velocity is greatest where the slope is greatest, right where it crosses the t axis. That means 2 pi t/T = 0, pi, 2 pi,...n pi. You can see that the maximum velocity occurs 1/4 priod ahead of the maximum displacement, so it is pi / 2 radians = 90o out of phase, a period = 2 pi radians=360o.

The period for a pendulum on earth is T = 2 pi sqrt(L/g)
The same equation holds with proper values of L and g on your planet.