Write down the kinetic energy and potential energy for a pendulum within the small angle approximation (cosø =1–5

Sine and cosine have period 2π.

(a) An oscillating object repeats its motion every 3.3 seconds. (i) What is the period of this oscillation? (ii) What is its frequency? (iii) What is its phase rate (i.e. angular frequency)? (b) A magnesium atom (mass of 24 proton masses) in a crystal is measured to oscillate with a frequency of roughly 10l3 Hz. What is the effective spring constant of the forces holding that atom in the crystal? (c) Sitting on a trampoline, a person with mass m sinks a distance Az below the trampoline's normal level surface. (i) If the person gently bounces on the trampoline (without leaving its surface), what would be the person's period of oscillation T? (You should not need the person's mass, but if you think you do, assume and state a value.) (ii) Find T for Az = 45 cm. Check: For Az = 20 cm you should find T = 0.90 s.

Shown here is a rod of length = 1.45 m and mass m = 678 g that is pivoted at one end. Centered on the other end of the rod is a solid sphere of radius R = 27 cm and the same mass as the rod. If this was turned into a physical pendulum with the given pivot, what would be the period of the pendulum?