Physics - SHM Question with Solution | TestHub

The formula for the time period is given as $\mathrm{T}=2\pi \sqrt{\frac{l}{\mathrm{g}}}$ The mass of displaced fluid is $\text{ Mass }=\text{ density }\times \text{ volume }$ $\mathrm{m}=\rho \times \mathrm{Al}$ At equilibrium, Weight of the block = Weight of the displaced liquid $\begin{array}{rl}& \therefore \mathrm{mg}=\mathrm{A}/\mathrm{pg}\\ & \therefore l=\frac{\mathrm{m}}{\mathrm{Ap}}\end{array}$ Substituting the values in the equation $\begin{array}{rl}& \mathrm{T}=2\pi \sqrt{\frac{l}{\mathrm{g}}}\\ & \mathrm{T}=2\pi \sqrt{\frac{\mathrm{m}}{\mathrm{A}\rho \mathrm{g}}}\end{array}$ The frequency $f=\frac{1}{T}$ $\therefore \mathrm{f}=\frac{1}{2\pi }\sqrt{\frac{\mathrm{Apg}}{\mathrm{m}}}$