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(A) When a block is connected to two springs on either side,any displacement $x$ of the block causes one spring to compress by $x$ and the other to st

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$[\frac{K_1 + K_2}{m}]^{1/2}$

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(A) When a block is connected to two springs on either side,any displacement $x$ of the block causes one spring to compress by $x$ and the other to stretch by $x$.Since both springs exert a restoring force in the same direction (opposing the displacement),the springs are effectively in a parallel configuration.The equivalent spring constant $K_{eq}$ is given by $K_{eq} = K_1 + K_2$.The angular frequency $\omega$ of a spring-mass system is given by $\omega = \sqrt{\frac{K_{eq}}{m}}$.Substituting the value of $K_{eq}$,we get $\omega = \sqrt{\frac{K_1 + K_2}{m}}$.

$A$ 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

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