Physics - SHM Question with Solution | TestHub

For a simple pendulum, restoring torque equates the $\begin{array}{rl}& \tau =-mgL\sin \theta =I\alpha \\ & \Rightarrow \alpha =-\frac{mgL}{m{L}^2}\sin \theta \approx -\frac{g}{L}\theta \\ & \alpha \approx -\left(\frac{g}{L}\right)\theta \Rightarrow \alpha =-{\omega }^2\theta =-\left(\frac{g}{L}\right)\theta \end{array}$ Force constant of an oscillating simple pendulum is given by $k=m{\omega }^2$ $k\propto m$ and $k\propto {\omega }^2=\left(\frac{g}{L}\right)$ Therefore, force constant of an oscillating simple pendulum is directly proportional to the mass of the bob.