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Frequency to Angular Frequency

A block of ma...

Question

A block of mass \(M\) is attached with tow springs as shown and oscillates. Surface is smooth. If the maximum velocity of blcok is \(v_0\) durign the motion, then amplitude of oscillation is

A

\frac{2 v_{0}}{3} \sqrt{\frac{M}{k}}

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B

v_{0} \sqrt{\frac{2 M}{3 k}}

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C

v_{0} \sqrt{\frac{M}{k}}

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D

\frac{2 v_{0}}{3} \sqrt{\frac{M}{k}}

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Solution

The correct option is C $v_{0} \sqrt{\frac{M}{k}}$
$\frac{1}{2} M v_{0}^{2} = \frac{1}{2} (3 k) A^{2}$
$A = v_{0} \sqrt{\frac{M}{3 k}}$

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