Initially, a block of mass m is at rest on a frictionless floor and the spring is in a relaxed condition. One end of the spring is rigidly attached to the block and the other end is fixed to a wall. A

Question

Initially, a block of mass m is at rest on a frictionless floor and the spring is in a relaxed condition. One end of the spring is rigidly attached to the block and the other end is fixed to a wall. A constant force is applied on the block as shown in the figure. The maximum velocity of the block is

TestHub · Accepted Answer

The block attains maximum speed when it passes through its equilibrium position.

$F = K x$

$x = \frac{F}{K}$

From work-energy theorem

$- \frac{1}{2} K {(\frac{K}{F})}^{2} + F (\frac{F}{K}) = \frac{1}{2} m v_{m a x}^{2}$

$\frac{F^{2}}{2 K} = \frac{1}{2} m v_{m a x}^{2}$

$v_{m a x} = \sqrt{\frac{F}{m K}}$

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