A particle is moving in SHM in a straight line. When the distance of the particle from equilibrium position has values `x_(1)` and `x_(2)` , the corresponding values of velocities are `u_(1)` and `u_(2)`. Show that time period of vibration is `T=2pi[(x_(2)^(2)-x_(1)^(2))/(u_(1)^(2)-u_(2)^(2))]^(1//2)`

Explanation

To show that the time period \( T \) of a particle in Simple Harmonic Motion (SHM) can be expressed as

\[ T = 2\pi \sqrt{\frac{x_2^2 - x_1^2}{u_1^2 - u_2^2}}, \]

we start with the relationship between velocity, displacement, and angular frequency in SHM.

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