Pendulum Motion

• the time it take to swing back and forth is called the period (T), measured in seconds
• the length (L) of the string affects the period
• the amplitude and mass has no affect on the period and gravitational acceleration (g) 
• the numbers of swing in a second is call the frequency (f), measure in hertz
• period is the reciprocal of frequency, T = 1/f

The equation of the period for small angle (< 15°) is given by T = 2pi √(L/g), g = 9.8 m/s^2

If L = 1 meter, T = 2 * 3.14 * √(1/9.8) =  2 seconds

If gravity is unknown, and given T and L, rearrange the equation above to solve for g:

g = 4 pi^2 (L/T^2)

The equation of the frequency is f = [√(L/g)] / 2pi 

f = [√(1/9.8)] / (2*3.14) = .05 Hertz (Hz)

Find the velocity at the bottom of the swing, apply potential energy =  kinetic energy: mgh = (1/2)mv^2, solve for v =  √(2gh), g = 9.8, h = vertical drop distance