A particle of mass 0.4 ~kg executes simple harmonic motion of amplitude 0.4 ~m . When it passes through the mean position, its kinetic energy is 256 10⁻³ ~J . If the initial phase of the oscillation is / 4 , then the equation of its motion is

Step-by-step solution

Given, mass of the particle, m=0.4 ~kg Amplitude, A=0.4 ~m Initial phase, = 4 Kinetic energy at mean position KE As, aligned & =256 10⁻³ ~J KE & = 1 2 m ^2 A^2 aligned where, is angular frequency. array cc & 1 2 m ^2 A^2=256 10⁻³ & 1 2 0.4 ^2 (0.4)^2=256 10⁻³ & ^2=8 & =2 2 rad s ⁻¹ array Equation of simple harmonic motion is given by aligned x & =A ( t+ ) & =0.4 [(2 2 ) t+ 4 ] aligned