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A constant force F is applied on a spring block system as shown in figure. The mass of the block is m and spring constant is k. The block is placed over a smooth surface. Initially the spring was unstretched. Choose the correct alternative(s)

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Time period of oscillation is

2 π \sqrt{\frac{m}{k}}

The block will execute SHM

The amplitude of oscillation is

\frac{F}{2k}

The maximum speed of block is

v = \sqrt{\frac{2 F x - k x^{2}}{m}}

answer is A, C, D.

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Detailed Solution

If execute SHM amplitude

x = \frac{F}{k}; T = 2 π \sqrt{\frac{m}{k}}

Work done due to force ‘F’

$F x = \frac{1}{2} {mv}^{2} + \frac{1}{2} k x^{2}$

$\Rightarrow \sqrt{\frac{2 F x - k x^{2}}{m}} = v$

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