Question

A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is $T$. If the spring is divided in two equal parts and one is used to continue the simple harmonic motion, the time period will

• A. Remain $T$
• B. Become $2T$
• C. Become $\frac{T}{2}$
• D. become $\frac{T}{\sqrt{2}}$

Answer 1

The correct option is D become $\frac{T}{\sqrt{2}}$

If a spring is divided into $n$ equal parts then its spring constant becomes $n$ times. So,

$T_i=2\pi \sqrt{\frac{m}{K}}{K}_j=2K$

So,

$T_f=2\pi \sqrt{\frac{m}{2K}}\frac{T_i}{T_f}=\sqrt{2}{T}_f=\frac{T}{\sqrt{2}}$