- The length of the simple Pendulum is the distance between the point where it is suspended and the centre of gravity of the heavy point mass.
- The simple Pendulum oscillates about its mean position at that time two forces acts on it which are
Gravitational force in downward direction
Tension in the string
- The time taken by the simple Pendulum to complete one oscillation is called as time period of simple Pendulum and it is given by
- T = 2π √L/g
Where, L is the length of the pendulum
g acceleration due to gravity
- The simple Pendulum whose time period is 2 seconds is called as seconds pendulum.
- Thus, for seconds pendulum L = g/π2.
- On the basis of time period of simple Pendulum there are some laws defined which are discussed as below.
Laws of Simple Pendulum:
Statement:
We know that, the time period of simple Pendulum is given by
T = 2π √L/g
1.) Law of length:
The law of length states that the time period of simple Pendulum is directly proportional to the square root of the length of the simple Pendulum.
That means, T α √L
2.) Law of acceleration due to gravity:
The law of acceleration due to gravity states that the time period of simple Pendulum is inversely proportional to the square root of the acceleration due to gravity.
That means, T α 1/√g
3.) Law of mass:
The law of mass states that the time period of simple Pendulum is not depending on the mass of the pendulum. That means whatever will be the mass of Pendulum but its time period remains same and does not vary with its mass.
4.) Law of isochronous:
Law of isochronous states that the time period of simple Pendulum does not depend on the amplitude of the simple Pendulum. That means whatever is the amplitude of the simple Pendulum but the time period does not vary with its amplitude.
Example:
If length of the simple Pendulum is 2m, mass of simple Pendulum is 20g then what will be it’s time period?
Solution:
We know that,
The time period of simple Pendulum is given by
T = 2π√L/g
T = 2*3.14*√2/9.8
T = 6.28*0.4516
T = 2.84 seconds
Thus, the time period of given simple Pendulum is 2.84 seconds.