Coupon Accepted Successfully!


Energy in SHM

A particle executing SHM possesses two types of energy: potential energy and kinetic energy.

Potential energy

Potential energy is an account of the displacement of the particle from its mean position. The restoring force F = –ky against which work has to be done.
So 60273.png
Important Points
  • Potential energy maximum and equal to total energy at extreme positions
    when y = ±aωt = π/2; t = T/4
  • Potential energy is minimum at mean position,
    Umin = 0, when y = 0; ωt = 0; t = 0

Kinetic energy

Kinetic energy is because of the velocity of the particle.
Kinetic energy,
  • Kinetic energy is maximum at mean position and equal to total energy at mean position.
60206.png when y = 0; t = 0; ω t = 0
  • Kinetic energy is minimum at extreme position.
Kmin = 0, when y = at = T/4, ωt = π/2;

Total energy

Total mechanical energy = Kinetic energy + Potential energy
E = 60200.png
Total energy is not a position function, i.e., it always remains constant.

Energy position graph

Kinetic energy (K60194.png
Potential Energy (U) = 60187.png
Total energy (E) = 62250.png
It is clear from Fig. 2 that
Fig. 2
  • Kinetic energy is maximum at mean position and minimum at extreme position.
  • Potential energy is maximum at extreme position and minimum at mean position.
  • Total energy always remains constant.
Kinetic energy
Potential energy
where ω = 2ω and 60136.png, i.e., in SHM, kinetic energy and potential energy vary periodically with double the frequency of SHM (i.e., with time period T = T/2).
From Fig. 3, we note that potential energy or kinetic energy completes two vibrations in a time during which SHM completes one vibration. Thus, the frequency of potential energy or kinetic energy is double than that of SHM.
Fig. 3

Test Your Skills Now!
Take a Quiz now
Reviewer Name