A particle of mass 10g executes a linear SHM of amplitude 5cm with a period of 2 s. Find the PE and KE…

Q: A particle of mass 10g executes a linear SHM of amplitude 5cm with a period of 2 s. Find the PE and KE, 1/6 s after crossing the mean position.

Sol: Given m = 10 g = 10-2 kg ,T = 2 s,

ω = 2π/T = 2π/2 = π rad/s

A = 5 cm = 5 × 10-2 m

$\large K.E = \frac{1}{2}m \omega^2 A^2 cos^2 \omega t $

At t=1/6 s ,

$\large K.E = \frac{1}{2}\times 10^{-2} \pi^2 (5 \times 10^{-2})^2 cos^2 \pi/6 $

= 9.25 × 10-5 J

$\large P.E = \frac{1}{2}m \omega^2 A^2 sin^2 \omega t $

$\large P.E = \frac{1}{2}\times 10^{-2} \pi^2 (5 \times 10^{-2})^2 sin^2 \pi/6 $

= 3.085 × 10-5 J