Question

A block of mass $1kg$ is connected with a smooth plank of the same mass is performing oscillations. The value of the spring constant is $200N{m}^{-1}$ . 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

Answer: 20

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