A block of mass 1   kg is fastened to a spring of spring constant of 100   N   m - 1 . The…

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
  1. 0.375 J,0.125 J
  2. 0.125 J,0.375 J
  3. 0.125 J,0.125 J
  4. 0.375 J,0.375 J

Solution

Angular frequency of SHM, ω=km=1001=10

Velocity, v=ωa2-x2=100.12-0.052

⇒v=0.866 m/s

Kinetic energy, K.E=12mv2=12×1×0.8662

⇒K.E=0.375 J

Potential energy, P.E=12kx2=12×100×0.052

⇒P.E=0.125 J

Asked in: AP EAMCET 2021 (19 Aug Shift 2)

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