First slide

Simple hormonic motion

Question

What will be the force constant of the spring system shown in fig. (7)

Moderate

A

$\frac{k_{1}}{2} + k_{2}$
B

${[\frac{1}{2 k_{1}} + \frac{1}{k_{2}}]}^{- 1}$
C

$[\frac{1}{2 k_{1}} + \frac{1}{k_{2}}]$
D

${[\frac{2}{k_{1}} + \frac{1}{k_{2}}]}^{- 1}$

Solution

$Two spritrgs of force constants k_{1} and k_{2} are in parallel . Hence k^{'} = k_{1} + k_{1} = 2 k_{1} The third spring is il series with spring of force constant k ∴ \frac{1}{k} = [\frac{1}{2 k_{1}} + \frac{1}{k_{2}}] or k = {[\frac{1}{2 k_{1}} + \frac{1}{k_{2}}]}^{- 1}$

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