PERIOD OF A PENDULUM

PERIODIC MOTION The motion which repeats itself after fixed time intervals is called periodic motion The best example of periodic motion are the pendulum clocks.

A SIMPLE PENDULUM A string with a mass at the end which is free to swing is called a pendulum.

LENGTH OF THE PENDULUM The length of the string from the point of suspension to the center of mass of the pendulum bob is called the length of the pendulum. It is denoted by L. The unit is meter.

AMPLITUDE OF THE PENDULUM The angle θ is called amplitude. It is measured from the maximum swing position to the vertical line. The unit is degree. θ

MASS OF THE PENDULUM m The mass of a pendulum bob is m. The unit is kg. m

OSCILLATION The motion of the mass from its extreme position A to C and back to A is called an oscillation.

PERIOD FOR ONE OSCILLATION The time taken for one oscillation is very short and therefore, difficult to measure accurately. To find the time taken, we find the time taken for large number say 10/20 oscillations. This time divided by 10/20 will give us time taken for one oscillation. The period is denoted as T. The unit of T is second.

LENGTH vs. PERIOD OF THE PENDULUM The graph of the relationship between length and time period of the pendulum is a parabola. Thus the relationship can be expressed as L=constant X T2

Pendulum Equation The Period of the pendulum T is related to the length L by the relation. This equation is only an approximation when amplitude θ is small.