# Syntax

# 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 (F_{g}sin(theta))

Inertia (I) = (1/12)ML^{2}

Period (T) = 2pi (sqrt(L / g) = 2pi(sqrt(I/mgh))

-L(mgsin(theta)) = I*(alpha)

Alpha = -(mgh / I) * theta

Velocity (v) = -wx_{m}sin(wt + phase constant or phase angle (phi))

Acceleration (a) = -w^{2}x_{m}cos(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.

For an example, follow this link:

http://farside.ph.utexas.edu/teaching/301/lectures/node96.html

# Applications

Use the pendulum to regulate the motion of the hands of a clock, such as in grandfather clocks. Everytime the pendulum swings the gear moves one notch and this leads to other gears moving the hands of the clock

# External Links

- [http://hyperphysics.phy-astr.gsu.edu/Hbase/balpen.html] - Further Explanation
- [http://www.school-for-champions.com/science/pendulum.htm] - Further Explanation
- [http://webphysics.davidson.edu/physlet_resources/bu_semester1/c12_ballistic.html] - This has a demonstration that you can watch