Regents Physics The Simple Pendulum

What is a Simple Pendulum? A simple pendulum consists of a bob or mass attached to a string of negligible mass  l m

Where do we find pendulums? We typically find them in clocks Very minimal friction Good for showing conservation of energy

The Foucault Pendulum Originally designed to measure the rotation of the Earth At either the North Pole or South Pole, the plane of oscillation of a pendulum remains fixed with respect to the fixed stars while Earth rotates underneath it, taking one sidereal day to complete a rotation. So relative to Earth, the plane of oscillation of a pendulum at the North or South Pole undergoes a full clockwise or counterclockwise rotation during one day, respectively. When a Foucault pendulum is suspended on the equator, the plane of oscillation remains fixed relative to Earth. At other latitudes, the plane of oscillation processes relative to Earth, but slower than at the pole; the angular speed, Animation of a Foucault pendulum, with the rotation rate greatly exaggerated. The green trace shows the path of the pendulum bob over the ground, and the blue trace shows the path in a frame of reference rotating with the plane of the pendulum.

Variables Involved Period (T) – The time required for the displaced pendulum to complete one cycle of motion – measured in seconds Frequency (f) – The number of cycles per second – measured in hertz (Hz) Frequency = 1/T Both are independent of mass Amplitude is displaced angle of distance

Pendulum Equation T = 2 l g This equation holds for amplitudes of less than 15 degrees

Energy in a Pendulum

Pendulum Practice Problem Calculate the length of a pendulum that posses a 2-second period and is displaced 15° from vertical 2) Choose Equation 1) Write knowns/unknowns T = 2 s g = 9.8 m/s2 3) Rearrange and solve end