The minimum time taken by a spring block system (having time period T) to travel a distance equal to amplitude of motion is equal to

Question

The minimum time taken by a spring block system (having time period T) to travel a distance equal to amplitude of motion is equal to (A) (T/4) (B) (T/6) (C) (T/8) (D) (T/10)

Tardigrade Admin · Accepted Answer

Velocity-time graph of a body executing S.H.M. is

Solution

So to cover a given distance in minimum time velocity should be greater. So it must be around mean position and minimum time taken to cover a distance

\frac{a}{2}

is

\frac{T}{12}

∴ T_{R e q u i re d} = \frac{T}{6}

Q. The minimum time taken by a spring block system (having time period T) to travel a distance equal to amplitude of motion is equal to

$\frac{T}{4}$

$\frac{T}{6}$

$\frac{T}{8}$

$\frac{T}{10}$

Velocity-time graph of a body executing S.H.M. is

So to cover a given distance in minimum time velocity should be greater. So it must be around mean position and minimum time taken to cover a distance $\frac{a}{2}$ is $\frac{T}{12}$
$∴ T_{R e q u i re d} = \frac{T}{6}$