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A mass m attached to a spring of spring ...

A mass m attached to a spring of spring constant `k` is stretched a distance `x_0` from its equilibrium position and released with no initial velocity. The maximum speed attained by mass in its subsequent motion and the time at which this speed would be attained are, respectively.

A

`sqrt((k)/(m))x_(0)` and `sqrt((m)/(k))`

B

`sqrt((k)/(m))(x_(0))/(2)` and `(pi)/(2)sqrt((m)/(k))`

C

`sqrt((k)/(m))x_(0)` and `(pi)/(2)sqrt((m)/(k))`

D

`sqrt((k)/(m))(x_(0))/(2)` and `pisqrt((m)/(k))`

Text Solution

Verified by Experts

The correct Answer is:
C
Amplitode =`x_(0)`,`omega=sqrt((k)/(m))`
Speed is maximum at mean `v_(max)=Aomega=x_(0)sqrt((k)/(m))`
Time taken to reach from extreme (initial position )to mean =`(T)/(4)=(1)/(4)2pisqrt((m)/(k))=(pi)/(2)sqrt((m)/(k))`
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