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Energy in SHM
Intermediate
Total energy is constant, swapping between kinetic and potential.
E = ½kA²Total energy E = ½kA² = ½mω²A² is constant, shared between kinetic ½mv² and potential ½kx². Energy doesn't depend on frequency alone.
k = 40, A = 0.1: E = 0.2 J.
Doubling the amplitude quadruples the energy.
In more detail
In SHM, the total energy is constant and equals ½kA², shared between kinetic and potential energy. At the extremes the energy is all potential, and at equilibrium it is all kinetic.
Real-world uses
- Designers check energy in vibrating structures to predict damage.
- Mechanical watch springs store energy that is released through oscillation.
- A mass on a spring is an example of energy swapping between motion and stretch, and the total energy stays constant when there is no friction.
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Frequently asked questions
Is energy conserved in ideal SHM?
Yes, in an ideal system without damping.
Does energy depend on the mass?
Not in the simple formula, only on the spring constant and amplitude.
Is the total energy in SHM constant?
Yes, without damping. The energy shifts between kinetic and potential forms but the total is ½kA².
Related topics in Oscillations & SHM
Torsional pendulum · Second's pendulum · Simple pendulum in elevator · Kinetic and potential energy in SHM · Average energy over a cycle · Differential equation of SHM