First slide

Applications of SHM

Question

Two springs of constant $k_{1}$ and $k_{2}$ are joined in series. The effective spring constant of the combination is given by

Easy

A

$\sqrt{k_{1} k_{2}}$
B

$(k_{1} + k_{2}) / 2$
C

$k_{1} + k_{2}$
D

$k_{1} k_{2} / (k_{1} + k_{2})$

Solution

In series combination
$\frac{1}{k_{S}} = \frac{1}{k_{1}} + \frac{1}{k_{2}} = \frac{k_{2} + k_{1}}{k_{1} k_{2}} \Rightarrow k_{S} = \frac{k_{1} k_{2}}{k_{1} + k_{2}}$ .

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