I don't want an answer I would just like to know what equations to use to answer the questions. It's confusing me. i. imgur. com/6CouaRj .png

Question

An astronaut lands on an alien planet. He places a pendulum (L = 0.200 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.
Show any necessary calculations.

thanks in advance

Answer 1

the period is 2 pi * square root of L/g

we know the length
however to find the period we need g
on the surface of earth g is about 9.81 m/s^3
HOWEVER on the moon for example is is only about one sixth of that so the period will be sqrt 6 longer
IN OTHER WORDS WE MUST KNOW g on this planet to find the period
frequency = 1/period

If you know the period, then of course you can find g
T = 2 pi sqrt (L/g local)
(T/2pi)^2 = L/g
g local = L /(T/2pi)^2

I can not see your graph of course but displacement and velocity are 90 degrees (pi/2) apart ad displacement and acceleration are 180 degrees (pi) apart
eg
if x = a sin wt
v = a w cos wt
(note cos wt=sin (wt+pi/2))
a = -a w^2 sin wt = -w^2 x
note sin (wt+pi) = -sin wt