Simple Harmonic Motion of Pendulums Practice Problems

The equation of SHM motion of a simple pendulum is derived using assumptions that make it valid for small displacements. During an experiment, you suspend a spherical ball using a 1.20 m long thread and displace the pendulum by 28°. Calculate the period of the pendulum assuming small displacement and using the equation . i) State the value that is more accurate, ii) Determine the percentage error in the other value by comparing it with the value you consider accurate. 

The motion of a simple pendulum approaches SHM for small displacements. Suppose you displace a sphere suspended from a 1.4 m long thread through 25.0°, i) what is its period assuming a small displacement? ii) What is the period using the given three terms of equation ?

A grandfather clock with a 1.00 m long pendulum hangs on a clock tower. The mass of the bob on the pendulum is 0.500 kg. An unlucky driver hits the tower vibrating it. If the pendulum was initially at rest in the equilibrium position, how many cycles per second will the pendulum make?

A plumb bob displaced by a small angle from the equilibrium position has a period of 1.23 s on the earth. What is the period of this simple pendulum when taken to the surface of planet K where g is 13.2 m/s²?

You construct a 0.84 m long simple pendulum using a light string then displace it by 4.30° on one side before releasing it to oscillate. Next, you double the displacement angle to 8.60° on the same side. What is the difference between the two time periods for the two angles used?

A simple pendulum has a length of 1.35 m. The pendulum is displaced to one side by 5.60° and allowed to oscillate. Determine the time taken from the time it is launched to the time its acceleration is zero.