First slide

Simple hormonic motion

Question

What will be the force constant of the spring system shown in the figure?

Moderate

A

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

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

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

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

Solution

For parallel combination of first two identical springs of spring constant $k_{1}$ , effective spring constant
$K_{p} = 2 k_{1}$
Now, springs of spring constants $k_{p} and k_{2}$ are joined in series, so the force constant or the spring constant of the system is
$\frac{1}{K_{S}} = \frac{1}{K_{P}} + \frac{1}{K_{2}} = {(\frac{1}{2 k_{1}} + \frac{1}{k_{2}})}^{- 1}$

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