A block of mass 1 kg is fastened to a spring of spring constant of 100 N m - 1 . The block is pulled to a distance x = 10 cm from its equilibrium position ( x = 0 cm ) on a frictionless surface, from rest at t = 0 . The kinetic energy and the potential energy of the block when it is 5 cm away from the mean position is

Step-by-step solution

Angular frequency of SHM, ω = k m = 100 1 = 10 Velocity, v = ω a 2 - x 2 = 10 0 . 1 2 - 0 . 05 2 ⇒ v = 0 . 866   m / s Kinetic energy, K . E = 1 2 m v 2 = 1 2 × 1 × 0 . 866 2 ⇒ K . E = 0 . 375   J Potential energy, P . E = 1 2 k x 2 = 1 2 × 100 × 0 . 05 2 ⇒ P . E = 0 . 125   J