Physics - SHM Question with Solution | TestHub

If we pull the mass $m$ towards right by a distance $x$ then the restoring force it experiences is $$\begin{array}{rl}F& =-kx\\ \Rightarrow m\frac{d^{2}x}{d{t}^2}& =-kx\\ \Rightarrow \frac{d^{2}x}{d{t}^2}+\frac{k}{m}x& =0\Rightarrow \frac{d^{2}x}{d{t}^2}+{\omega }^{2}x=0\\ \text{ Where }\omega & =\sqrt{\frac{x}{m}}\\ \Rightarrow \frac{2\pi }{T}& =\sqrt{\frac{x}{m}}\\ \Rightarrow n& =\frac{1}{2\pi }\sqrt{\frac{x}{m}}\end{array}$$