Question: The angle of the pendulum in Figure is given by . If at t = 0 , and ,

1. what is the phase constant ,
2. what is the maximum angle ?

(Hint: Don’t confuse the rate at which changes with the of the SHM.)

For Equation , suppose the amplitude is given by

where is the (constant) amplitude of the external oscillating force exerted on the spring by the rigid support in Figure below. At resonance,

1. what is the amplitude of the oscillating object?
2. what is the velocity amplitude of the oscillating object?

In Fig. 15-64 , a 2500 Kg demolition ball swings from the end of a crane. The length of the swinging segment of cable is 17m . (a) Find the period of the swinging, assuming that the system can be treated as a simple pendulum. (b) Does the period depend on the ball’s mass?

Hanging from a horizontal beam are nine simple pendulums of the following lengths.

Suppose the beam undergoes horizontal oscillations with angular frequencies in the range from

to

A block of mass, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant. A bullet of massand velocityof magnitudstrikes and is embedded in the block (SeeFigure). Assuming the compression of the spring is negligible until the bullet is embedded.

(a) Determine the speed of the block immediately after the collision and

(b) Determine the amplitude of the resulting simple harmonic motion.

Question: In Figure, the pendulum consists of a uniform disk with radius r = 10.cm and mass 500 gm attached to a uniform rod with length L =500mm and mass 270gm.

1. Calculate the rotational inertia of the pendulum about the pivot point.
2. What is the distance between the pivot point and the center of mass of the pendulum?
3. Calculate the period of oscillation.