Physics - SHM Question with Solution | TestHub

The spring constant $k$ is given by the ratio of the applied force to the extension produced:

$k=\frac{F}{x}$

The time period of vertical oscillations of a mass $m$ suspended from the spring is:

$T=2\pi \sqrt{\frac{m}{k}}$

Squaring both sides:

$T^2=4{\pi }^2\frac{m}{k}$

Substituting the value of $k$:

$T^2=4{\pi }^2\frac{m}{\frac{F}{x}}=\frac{4{\pi }^{2}mx}{F}$

Rearranging to solve for the mass $m$:

$m=\frac{T^{2}F}{4{\pi }^{2}x}$

Answer: $\frac{T^{2}F}{4{\pi }^{2}x}$