Time Period of Simple Pendulum

Dear student,

In the diagram , we have exaggerated the distance y of the pendulum from the mean position. Since the string is of infinite length, the oscillation will be a straight line tangential to earth. And the string of  infinite length will be always be perpendicular to the line of oscillation of the pendulum. Now let us see the derivation:

Because the pendulum is very close to the surface of earth, the gravitational force on the pendulum is:

F= mg

The Fx component will be balanced by the the tension T in the string.

The Fy component will cause the oscillation.

Equation of motion:

The above equation represents a simple harmonic motion, whose time period is given by:

Hope this helps.

Regards

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