First slide

Applications of SHM

Question

A block is placed on a frictionless horizontal table. The mass of the block is m and springs are attached on either side with force constants $K_{1}$ and $K_{2}$ . If the block is displaced a little and left to oscillate, then the angular frequency of oscillation will be

Moderate

A

${(\frac{K_{1} + K_{2}}{m})}^{1 / 2}$
B

${[\frac{K_{1} K_{2}}{m (K_{1} + K_{2})}]}^{1 / 2}$
C

${[\frac{K_{1} K_{2}}{(K_{1} - K_{2}) m}]}^{1 / 2}$
D

${[\frac{K_{1}^{2} + K_{2}^{2}}{(K_{1} + K_{2}) m}]}^{1 / 2}$

Solution

In this case springs are in parallel, so $k_{eq} = k_{1} + k_{2}$
and $ω= \sqrt{\frac{k_{eq}}{m}} = \sqrt{\frac{k_{1} + k_{2}}{m}}$

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