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 KE of the particle at a point which is at a distance equal to 1/3 of its

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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 KE of the particle at a point which is at a distance equal to 1/3 of its amplitude from its mean position is

TestHub · Accepted Answer

Displacement of particle in the case of SHM

$y = A \sin (ω t)$ ...(i)

$y = 3 \sin (0.2 t)$ ...(ii)(given)

Comparing Eqs. (i) and (ii), we get

$A = 3, ω = 0.2$

Now, particle distance $x = \frac{A}{3} = 1$

Kinetic energy in SHM

= $\frac{1}{2} m ω^{2} (A^{2} - x^{2})$

= $\frac{1}{2} \times 3 \times 10^{- 3} {(0.2)}^{2} [3^{2} - 1^{2}]$

$= 0.48 \times 10^{- 3}$ J

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