A particle of mass m is released from rest and follows a parabolic path as shown in Fig. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time?
 

Solution:

Restoring force $\mathrm{F}=-\mathrm{mg} \sin \mathrm{\theta }$
Equation of curve $\mathrm{y}={\mathrm{cx}}^2$

                          $\tan \mathrm{\theta }=\frac{\mathrm{dy}}{\mathrm{dx}}=2\mathrm{cx}$
For small angle, $$\begin{gathered} \sin \mathrm{\theta }=\tan \mathrm{\theta }=2 \mathrm{cx} \\ \mathrm{F}=-\mathrm{mg}\left(2 \mathrm{cx}\right)\Rightarrow \mathrm{F}\propto -\mathrm{x} \end{gathered}$$
Since particle is executing SHM in a potential well after released from maximum displacement position.