# Pendulum Formula

Pendulum

A simple pendulum is a mechanical arrangement that demonstrates periodic motion. The simple pendulum comprises of a small bob of mass ‘m’ suspended by a thin string secured to a platform at its upper end of length L.

The string’s mass is thought of to be negligible paralleled to the mass of the bob and is disregarded. The bob when released from a specific height swings back and forth over the same path.

The pendulum bob travels along a circular arc instead of to and fro in a straight line. Though when the oscillations are minor, the motion of the bob is straight.

The restoring force that causes the pendulum to go through simple harmonic motion is essentially the gravitational force constituent which is tangent to the path of motion.

Frequency= 1T

The period of such pendulum is articulated as

T = 2πLg−−√2πLg

Where, period of pendulum(seconds) = T

Length of the pendulum string (m) = And

acceleration due to gravity (m/s2) = ‘g

Solved Examples

Some sample problems on Pendulum are:

Problem 1: Find the time period of the bob with a string length of 0.75 m. The gravitational constant = 9.8 m/s2?

$Time\;Period=2*(\frac{22}{7})*\frac{\sqrt{0.75}}{9.8}$

$Time\;Period=6.3\sqrt{0.07653}=6.3\times&space;0.2766=1.7428Seconds$

Problem 2: Find the length of the string when the time period of the simple pendulum is found to be 1.5 seconds. The gravitational constant is taken as 9.8 m/s2?

$(Time\;Period)1.5s=2*(\frac{22}{7})\sqrt{\frac{L}{9.8(\frac{m}{s^{2}})}}$
$Length=0.56m$