Question

3. 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.

Answer 1

a).  We could read off the period if we had the graph.
      The frequency is 1/period.

b).  The velocity is the first derivative of the displacement,
       so it should lag the displacement by 90° .
 
       The acceleration is the derivative of the velocity,
        so that puts it 180° behind the displacement.

c).  If we could see the graph, then, knowing the pendulum's
      length and the period of its swing, we could calculate the
      acceleration of gravity on the planet at which he is at.

      The number of 'G-forces' is

                   9.8 m/s² / (acceleration of gravity where he is at) .

       The number is a ratio ... without units.