Question

1. A simple pendulum on the surface of Earth is found to undergo 18.0 complete small‑amplitude oscillations in 7.45 s. Find the pendulum's length ?.

2. A simple pendulum with a period ?=4.00s is attached to the ceiling of an elevator which is initially at rest. The acceleration due to gravity is ?=9.81 m/s2.

a) Calculate the oscillation period ?up when the elevator begins to accelerate upwards with acceleration ?=2.00 m/s2.

b) Calculate the oscillation period ?down when the elevator accelerates downwards with acceleration ?=2.00 m/s2

3a. An undamped 1.84 kg horizontal spring oscillator has a spring constant of 39.2 N/m. While oscillating, it is found to have a speed of 3.64 m/s as it passes through its equilibrium position. What is its amplitude ? of oscillation?

3b. What is the oscillator's total mechanical energy ?tot as it passes through a position that is 0.734 of the amplitude away from the equilibrium position?

4a. A physics lab is demonstrating the principles of simple harmonic motion (SHM) by using a spring affixed to a horizontal support. The student is asked to find the spring constant, ?. After suspending a mass of 295.0g from the spring, the student notices the spring is displaced 37.5cm from its previous equilibrium. With this information, calculate the spring constant.

4b. When the spring, with the attached 295.0g mass, is displaced from its new equilibrium position, it undergoes SHM. Calculate the period of oscillation, ? , neglecting the mass of the spring itself.

Answer 1