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An unhappy mouse of mass m_o moving on the end of a spring of spring constant p is acted upon by a damping force $F_{x} = - {bv}_{x}$ . For what value of b the motion is critically damped ?

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$b = \sqrt{\frac{p}{m_{0}}}$

$b = 2 \sqrt{{pm}_{o}}$

$b = \sqrt{\frac{P^{2}}{2 m_{o}}}$

$b = \sqrt{\frac{P}{2 m_{o}}}$

answer is B.

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Detailed Solution

The condition for critical damping is b² = 4mK
but K is given to be P so b² = 4mp
$b = 2 \sqrt{mp}$

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