A block of mass m rigidly attached with a spring k is compressed through a distance A. If the block is released, the period of oscillation of the block for a complete cycle is equal to

A block of mass m rigidly attached with a spring k is compressed throu

1.	A block of mass m rigidly attached with a spring k is compressed through a distance A. If the block is released, the period of oscillation of the block for a complete cycle is equal to
Answer» `(4pi)/(3)sqrt((m)/(k))` `(pi)/(sqrt(2))sqrt((m)/(k))` `(2pi)/(3)sqrt((m)/(k))` None of these Solution :The period of MOTION from `A` to `O` is equal to quarter of the time period `T` of OSCILLATION of mass spring system. `rArr t_(AO)=(T)/(4)=(1)/(4)[2pisqrt((m)/(k))]=(pi)/(2)sqrt((m)/(k))` Since the motion is simple harmonic `OB=OAsin"(2pi)/(T)t_(OB)`, where `t_(OB)` is the time of motion from `O` to `B`. `rArr t_(OB)=(T)/(2pi)sin^(-1)"(A//2)/(A)=(T)/(2pi)((pi)/(6))` `=(T)/(12)=(2pi)/(12)sqrt((m)/(k))=(pi)/(6)sqrt((m)/(k))` `:. ` The TOTAL time of motion for a complete CYCLE `=t=2(t_(AO)+t_(OB))` `rArr t=2[(pi)/(2)sqrt((m)/(k))+(pi)/(6)sqrt((m)/(k))]=(4pi)/(3)sqrt((m)/(k))`.