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  4. 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 part is used to continue the simple harmonic motion, the time period will

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Q. 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 part is used to continue the simple harmonic motion, the time period will

Oscillations

Solution:

$\frac{1}{k'}+\frac{1}{k'}=\frac{1}{k} $
$\Rightarrow k'=2 k$
$T=2 \pi \sqrt{\frac{m}{k}}$ and $T'=2 \pi \sqrt{\frac{m}{2 k}}$
$\frac{T'}{T}=\frac{1}{\sqrt{2}}$ or $T'=\frac{T}{\sqrt{2}}$