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Two springs are connected to block of mass M placed on a frictionless surface as shown below. If both the springs have a spring constant kkk​. the fre
Question

Two springs are connected to block of mass M placed on a frictionless surface as shown below. If both the springs have a spring constant kk. the frequency of oscillation of the block is:

A.

(12π)k2M\left(\frac{1}{2 \pi}\right) \sqrt{\frac{k}{2 M}}​​

B.

(12π)kM\left(\frac{1}{2 \pi}\right) \sqrt{\frac{k}{M}}​​

C.

(12π)2kM\left(\frac{1}{2 \pi}\right) \sqrt{\frac{2 k}{M}}​​

D.

(12π)Mk\left(\frac{1}{2 \pi}\right) \sqrt{\frac{M}{k}}​​

Correct option is C

Given:Block of mass MTwo springs connected in parallel, each with spring constant kThe frequency of oscillation is required.Concept Used:When two springs are connected in parallel, their effective spring constant is the sum of the individual spring constants:Keq=k+k=2k\textbf{Given:}\\\begin{aligned}&\text{Block of mass } M \\&\text{Two springs connected in parallel, each with spring constant } k \\&\text{The frequency of oscillation is required.}\end{aligned}\\\textbf{Concept Used:}\\\begin{aligned}&\text{When two springs are connected in parallel, their effective spring constant is the sum of the individual spring constants:} \\&K_{\text{eq}} = k + k = 2k\end{aligned}​​The frequency of oscillation ω for a mass-spring system is given by:ω=KeqM=2kMThe frequency of oscillation is the natural frequency of the system, and it is inversely related to the square root of the mass and directly related to the spring constant.Using the formula for the frequency, we substitute Keq=2k into the equation:ω=2kM\text{The frequency of oscillation } \omega \text{ for a mass-spring system is given by:} \\\omega = \sqrt{\frac{K_{eq}}{M}} = \sqrt{\frac{2k}{M}} \\\text{The frequency of oscillation is the natural frequency of the system, and it is inversely related to the square root of the mass and directly related to the spring constant.} \\\text{Using the formula for the frequency, we substitute } K_{eq} = 2k \text{ into the equation:} \\\omega = \sqrt{\frac{2k}{M}}​​

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