Question

A block of mass $1 \, kg$ is connected with a smooth plank of the same mass is performing oscillations. The value of the spring constant is $200 \, N \, m^{- 1}$ . The block and the plank are free to move and there is no friction anywhere. The angular frequency of the oscillation is $\omega \, rad \, s^{- 1}$ . Find the value of $\omega $ .

Answer 1

Using the concept of reduced mass, we obtain:-
$\omega =\sqrt{\frac{k}{m_{reduced}}}=\sqrt{\frac{2 k}{m}}\left(\because m_{reduced} = \frac{m \times m}{m + m} = \frac{m}{2}\right)$
$\Rightarrow \omega =\sqrt{\frac{2 \times 200}{1}}=20rads^{- 1}$