Question

An astronaut lands on an alien planet. He uses a pendulum (L = 1.5m) to produce simple harmonic motion, as shown in this graph.

Answer the following questions showing all work!

a. What is the period and frequency of the pendulum’s motion? (Time on the graph which is on the x axis is in seconds)

b. At what times will the pendulum be at its equilibrium point?

c. What is the acceleration due to gravity on the surface of the planet in m/s2?

10 Displacement -Velocity -Acceleration 10

Answer 1

There are two force on the pendulum of mass (m), mg and Tension in string T = mg cos Theta therefore acting opposite to the motion is mg sin Theta F = -mg sin Theta for small oscillation (i.e. simple Harmonic oscillation Theta rightarrow 0 (very small) for Theta rightarrow 0 sin Theta rightarrow Theta F = -mg Theta in triangle ABC Theta = x/L m/L d^2 x/dt^2 = -mg x/L rightarrow d^2 x/dt^2 + g/L x = 0 d^2 x/dt^2 + w^2 x = 0 --- (1) when x^2 = g/L rightarrow w = squareroot g/L Time period T = 2 pi/w = 2 pi squareroot L/g The solution of equation (1) x = A sin wt