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

Step-by-step solution

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 = A 3 = 1 Kinetic energy in SHM = 1 2 m ω 2 ( A 2 - x 2 ) = 1 2 × 3 × 10 - 3 0.2 2 [ 3 2 - 1 2 ] = 0.48 × 10 - 3 J