Physics - SHM Question with Solution | TestHub

When the mass $m$ is displaced by a small distance $x$ from its equilibrium position, one spring is stretched by $x$ while the other is compressed by $x$.

Both springs exert a restoring force in the same direction, opposite to the displacement.

The total restoring force on the mass is:

$F=-2kx-kx=-3kx$

The equivalent spring constant of the system is:

$k_{eq}=3k$

The frequency of oscillation is given by:

$f=\frac{1}{2\pi }\sqrt{\frac{k_{eq}}{m}}=\frac{1}{2\pi }\sqrt{\frac{3k}{m}}$

Answer: $\frac{1}{2\pi }\sqrt{\frac{3k}{m}}$