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Grade 12th passGeneral Physics

a particle starting fom mean position executes shm with a period of 8sec.The minimum time in which its potential energy becomes half of the total energy is

sri

8 Years agoGrade 12th pass

1 Answer

Eshan

8 Years ago

Time period of SHM= $\dfrac{2\pi}{\omega}=8 seconds\implies \omega=\dfrac{\pi}{4}Hz$

Potential energy of particle is half of the total energy.

$\implies \dfrac{1}{2}kx^2=\dfrac{1}{2}\times \dfrac{1}{2}kA^2$
Hence position at which the potential energy is half of total energy is $x=\dfrac{A}{\sqrt{2}}$

$x=Asin(\omega t )=\dfrac{A}{\sqrt{2}}$
$\implies \omega t=\dfrac{\pi}{4} \implies t=1s$

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