The displacement of a particle of mass 0 . 1   kg is, y = 0 . 05 sin 4 π 5 t + 0 . 4 (where all the quantities are in SI unit). Period of motion is 0 . 1   s . The total energy of the particle is,

Step-by-step solution

Given, the mass of the particle, m = 0 . 1   kg and the displacement, y = 0 . 05 sin 4 π 5 t + 0 . 4 and time period, T = 0 . 1   s . Now, comparing it with the equation of displacement of SHM , y = A sin ω t . It means, A = 0 . 005   m , ω = 20 π . Now, the formula of total energy is, T . E . = 1 2 m ω 2 A 2 = 1 2 × 0 . 1 × 20 π 2 × 0 . 005 2 = 0 . 05 π 2   J