Physics - NLM Question with Solution | TestHub

On the right hand side of the block, springs are connected in parallel $\therefore$ Their effective spring constant is given by $$\begin{array}{rl}& {\mathrm{K}}_1=\mathrm{K}+2\mathrm{K}\\ & {\mathrm{K}}_1=3\mathrm{K}\end{array}$$ On the left hand side of the block, springs are connected in series. $\therefore$ Their effective spring constant is given by, $$\begin{array}{rl}& \frac{1}{{\mathrm{K}}_2}=\frac{1}{2\mathrm{K}}+\frac{1}{2\mathrm{K}}\\ \therefore {\mathrm{K}}_2& =\mathrm{K}\end{array}$$ $\therefore$ Effective spring constant of the system is given by, $$\begin{array}{rl}& {\mathrm{K}}_{\mathrm{E}}=3\mathrm{K}+\mathrm{K}=4\mathrm{K}\\ \therefore \omega & =\sqrt{\frac{{\mathrm{K}}_{\mathrm{E}}}{\mathrm{M}}}=\sqrt{\frac{4\mathrm{K}}{\mathrm{M}}}\\ \therefore \mathrm{f}& =\frac{\omega }{2\pi }=\frac{1}{2\pi }\sqrt{\frac{4\mathrm{K}}{\mathrm{M}}}\end{array}$$