Time period of simple pendulum

Rohit and Rakesh were two friends.

They were watching time by a wall clock.

Then, Rohit observed that the motion of the pendulum is repeating within a certain time.

So, he asked his friend Rakesh what we can call this time.

Then, Rakesh replied that it is known as the time period of that pendulum.

Let's understand the time period of a simple pendulum

A pendulum is a weight suspended from a pivot so that it can swing freely.

Suppose, we have a pendulum with a small bob of mass as.

It is suspended from a light string of length which is fixed at its upper end.

Now, if we change the position of bob then there will swing in the bob.

And when the bob is at extreme position , the net force is not zero.

Then, the forces acting on the bob at the extreme position is,

The weight of the bob acting vertically downward.

The weight of the bob acting vertically downward.

And the tension of the string acting along the direction of the string.

The weight of the bob can be resolved into two rectangular components.

The two components of weight are and .

The horizontal component of weight is as,

And the vertical component of weight can be defined as.

So, the net force on the bob is tangent to the arc and can be given as

And for the angles less than about , the angle is approximately equal , so the restoring force will be

The displacement is directly proportional to theta.

And is expressed in radians, the arc length in a circle is related to its radius,

So, for the small angles, the restoring force is as

The restoring force of spring is as,

And the time period of the spring is as,

On comparing the simple pendulum with spring, the value of the spring constant is,

We get the time period of the simple pendulum as,

So, the time period of the simple pendulum is as,

Let's discuss the factors affecting the time period of a simple pendulum

The first factor is the length. The time period is directly proportional to the square root of the length of the pendulum.

The second factor is acceleration. The time period is inversely proportional to the square root of acceleration due to gravity.

Revision

The time period of a simp0le pendulum can be defined as.

The time period of the simple pendulum is directly proportional to the square root of the length.

The time period of the simple pendulum is inversely proportional to the square root of the acceleration due to gravity.

The end