## Period of a Simple Pendulum

The time taken by the bob to complete one vibration, is called the time period of the pendulum. It is represented by the symbol T . The time period of a simple pendulum is expressed by the formula

T = 2πlg−−√

wherel is the length of the pendulum and g is the acceleration due to gravity.

where

## Frequency of a Simple Pendulum

The number of
vibrations made by the bob in one second, is called the frequency of the
pendulum. It is represented by the symbol ν . Its S.I unit is per sec. Which has special name hertz (Hz).

Hence,

ν = 1T

or

## Simple Pendulum Equation

The equation for time period and frequency are

Time period, T = 2πlg−−√

Frequency, ν = 1T = 12πgl−−√

## Pendulum Gravity

The pendulum is
the instrument choice for gravity measurement. A simple pendulum is a
mass on the end of a cord or string. Put into motion by raising the mass
to the side, the mass is attracted by the earth. The variation in the
length and time are depends on the local attraction of gravity.

## Simple Pendulum Problems

### Solved Examples

**Question 1:**If a pendulum takes 4 sec to swing in each direction, find the length of the pendulum.

**Solution:**

Solution:

Given T=4 sec

We know that, T = 2πlg−−√

we can obtain the equation for length (l ),

=9.8×424π2 = 3.97 m

The length of the pendulum is 3.97 .

**Question 2:**What will be the value of the frequency of simple pendulum in a gravity free space?

**Solution:**

We know that T = 2πlg−−√

Frequency ν = 1T = 12πgl−−√

In gravity free space the value of g is zero.

Hence ν=0

The frequency in the gravity free space is zero.