Question

For the pendulum system below, suppose that the mass of the pendulum bob is 1.0 kg and the length of the string is 2.0 m. The pendulum is released from rest where θ = 5° = 0.087 rad and it swings back and forth. Assume air resistance is negligible.

(A) how man oscillation does the pendulum make in 20.0 seconds?

(B) what is the KE of the pendulum at t = 0.160 seconds?

(C) at what locations is the pendulum in motion (relative to equilibrium) does V = Vmax/2?

Answer 1

The equation of motion for small angle approximation
   
And so,
the solution of the equation with
  
we get
   
where,
   
And so, we have the time period of the motion
   
So, given the values, L = 2.0 m, g = 9.8 m/s^2, we get
   
And so, the time period is
   

A)

And so, the number of oscillation in time t = 20 seconds
   

B)

The kinetic energy is
  
And so for m = 1.0 kg, at time t = 0.160 seconds, we have
     
  

C)

The potential energy

And
   
And so, for