Question

Two identical springs of spring constant k are attached to a block of mass m and to fixed support. Show that when the mass is displaced from its equilibrium position then either side,it executes a simple harmonic motion. Find the period of oscillation.

Answer 1

Dear student,$$\begin{gathered} Ifwedisplacethemassinanydirection,theotherspringwillpullitbackduetorestoringforce. \\ TheforceifF=-kx \\ ontheotherhandF=mffromnewtonssecondlaw \\ thereforemf=-kx \\ f=\frac{-k}{m}x \\ thisisarepresentationofSHMwhereaccelerationisproportionaltothedisplacement. \\ andthefrequency\omega =\sqrt{\frac{k}{m}} \\ ifperiodofoscillationisT \\ then\omega =\frac{2\pi }{T}=\sqrt{\frac{k}{m}} \\ T=\frac{2\pi }{\sqrt{\frac{k}{m}}} \end{gathered}$$
Regards