A mass m is attached to two springs as shown | vedclass

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(C) When the mass $m$ is displaced to the right by a distance $x$,the spring with constant $K_1$ is compressed by $x$,and the spring with constant $K_

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$2 \pi \sqrt{\frac{m}{K_1+K_2}}$

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(C) When the mass $m$ is displaced to the right by a distance $x$,the spring with constant $K_1$ is compressed by $x$,and the spring with constant $K_2$ is stretched by $x$.Both springs exert a restoring force in the left direction.The total restoring force $F$ is given by:$F = -(K_1 x + K_2 x) = -(K_1 + K_2)x$Comparing this with the standard equation for simple harmonic motion,$F = -K_{eff} x$,we get the effective spring constant $K_{eff} = K_1 + K_2$.The acceleration $a$ of the mass is:$a = \frac{F}{m} = -\left(\frac{K_1 + K_2}{m}\right)x$Since $a = -\omega^2 x$,the angular frequency $\omega$ is:$\omega = \sqrt{\frac{K_1 + K_2}{m}}$The time period $T$ is given by:$T = \frac{2 \pi}{\omega} = 2 \pi \sqrt{\frac{m}{K_1 + K_2}}$

$A$ mass $m$ is attached to two springs as shown in the figure. The spring constants of the two springs are $K_1$ and $K_2$. For the frictionless surface,the time period of oscillation of mass $m$ is

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