Question

Why do we take small oscillations while measuring time period?​

Answer 1

Lets assume that we want to calculate the time period of a pendulum undergoing oscillations.

• Now, we need to make sure that the oscillations of the bob of the pendulum needs to be small.

• This is because only in this assumption we can consider that the pendulum is undergoing simple harmonic motion.

• As a result , the force will be directly proportional to negative of the small displacement.

$\boxed{ \bf \: F \: \propto \: - x}$

• And whenever we can assume simple harmonic motion the time period can be simply calculated as follows :

$\boxed{ \bf \: T = 2\pi \sqrt{ \dfrac{l}{g} } }$

Hope It Helps