1. Tardigrade
  2. Question
  3. Physics
  4. The displacement of a particle of mass 3 g executing simple harmonic motion is given by Y=3 sin (0.2 t) in SI units. The kinetic energy of the particle at a point which is at a distance equal to (1/3) of its amplitude from its mean position is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The displacement of a particle of mass $3 \,g$ executing simple harmonic motion is given by $Y=3 \sin (0.2\, t)$ in $SI $ units. The kinetic energy of the particle at a point which is at a distance equal to $\frac{1}{3}$ of its amplitude from its mean position is

Punjab PMETPunjab PMET 2008Oscillations

Solution:

Equation of $SHM , Y=3 \sin (0.2 t )$
Comparing with $Y=a \sin \omega t$, we have
$a=3\, m, \omega=0.2 \,s^{-1}$
Mass of the particle $=3 g =3 \times 10^{-3} kg$
Therefore, kinetic energy of the particle is
$K=\frac{1}{2} m \omega^{-3}\left(a^{2}-x^{2}\right) $
$=\frac{1}{2} \times 3 \times 10^{-3} \times(0.2)^{2}\left(3^{2}-1^{2}\right)$
$\left(\because x=\frac{1}{3}\right) $
$=0.48 \times 10^{-3} \,J$