I think you mean the energy of a particle attached to a spring. In that case the total energy is given by
E=K+P=12mv2+12kx2E=K+P=12mv2+12kx2Where mm is the mass of the particle, vv is the velocity of the particle, and xx is the distance of the particle from the origin. So, the maximum of potential energy PP is given when the kinetic energy KKis zero (i.e. when v=0v=0, in the turning points of the particle). In that case E=PmaxE=Pmax. SoE=Pmax=12kx2maxE=Pmax=12kxmax2here xmaxxmax is the maximum stretch of the spring (i.e. the turning point, v=0v=0).In the other hand, the maximum of kinetic energy is given when P=0P=0 (it occurs when x=0x=0), i.e. E=KmaxE=Kmax, or
E=Kmax=12mv2maxE=Kmax=12mvmax2where vmaxvmax is the maximun velocity of the particle, it occurs when the particle passes through the origin (i.e. when x=0x=0).Answer:
The maximum amount of potential energy and the maximum amount of kinetic energy are equal.
Explanation:
Kinetic energy and potential energy at its maximum are equal.
