Pendulum

# Overview

Pendulums fall into a class of simple harmonic oscillators in which the elasticity is due to gravity rather than that of a spring or twisted wire being compressed or stretched. The Simple Pendulum consists of a mass suspended at the end of a massless string that is fixed at one end. A Physical Pendulum can have a complicated distribution of mass suspended at the end of a massless string and the movements don't necessarily have to move from left to right.

# Equations

Torque = -Length (L)(Force of gravity (Fgsin(theta))
Inertia (I) = (1/12)ML2
Period (T) = 2pi (sqrt(L / g) = 2pi(sqrt(I/mgh))
-L(mgsin(theta)) = I*(alpha)
Alpha = -(mgh / I) * theta
Velocity (v) = -wxmsin(wt + phase constant or phase angle (phi))
Acceleration (a) = -w2xmcos(wt + phi)

A physical pendulum consists of a meter stick that is pivoted at a small hole drilled through a stick a distance d from the 50 cm mark. The period of oscillation is 2.5s find d.

A pendulum is formed by pivoting a long string of length L, that is massless about a point on the string that is a distance d above the center of the string. (a) Find the period of this pendulum in terms of d, L, and g, assuming small-amplitude swinging. What happens to the period if (b) d is decreased, or (c) L is increased

# Special Cases

A Special Case would be the ballistic pendulum. The ballistic pendulum consists of a mass with a velocity v providing a force to a mass suspended at the end of a string through elastic collision.