A simple pendulum consists of a bob of mass of 0.85 kg attached to a string of length 1.5 m.  The pendulum is raised to point Q, which is 0.08 m above its lowest position, and released so that it oscillates with a small amplitude θ between the points P and Q as shown below.   Draw free-body diagrams showing and labeling the forces acting on the bob in each situation. When it is at point P.  When it is at the lowest point.  Calculate the speed of the bob at the lowest point.  Calculate the total energy of the oscillating system.  Determine the height at which the potential and kinetic energies are equal.  Describe one modification that can be made to double the period of the oscillation. Explain.

A simple pendulum consists of a bob of mass of 0.85 kg attached to a string of length 1.5 m.  The pendulum is raised to point Q, which is 0.08 m above its lowest position, and released so that it oscillates with a small amplitude θ between the points P and Q as shown below.

1.   Draw free-body diagrams showing and labeling the forces acting on the bob in each situation.
   1. When it is at point P. 
   2. When it is at the lowest point. 
2. Calculate the speed of the bob at the lowest point. 
3. Calculate the total energy of the oscillating system. 
4. Determine the height at which the potential and kinetic energies are equal. 
5. Describe one modification that can be made to double the period of the oscillation. Explain.