Simple Pendulum info

Simple Pendulum info

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

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

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
νT=1

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

The following are the problems of simple pendulum.

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 
g=9.8 m/s

We know that,  T = 2πlg 
 we can obtain the equation for length (l),
l = gT24π2
=9.8×424π2 = 3.97m

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.

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