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  4. A simple harmonic oscillator consists of a particle of mass m and an ideal spring with spring constant k. The particle oscillates with a time period T. The spring is cut into two equal parts. If one part oscillates with the same particle, the time period will be

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Q. A simple harmonic oscillator consists of a particle of mass $m$ and an ideal spring with spring constant $k$. The particle oscillates with a time period $T$. The spring is cut into two equal parts. If one part oscillates with the same particle, the time period will be

Oscillations

Solution:

Time period of oscillator,
$T=2 \pi \sqrt{\frac{m}{k}}$
As $k \propto \frac{1}{l}$ (where, $l$ is the length of spring)
$\because k'=2 k$
$\therefore T'=2 \pi \sqrt{\frac{m}{2 k}}$
$=\frac{1}{\sqrt{2}} T$