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Kinetic and potential energy in SHM
Intermediate
Variation with displacement and time.
K = ½k(A² − x²), U = ½kx². K is maximum at the centre; U at the ends. They are equal at x = ±A/√2.
At A/√2, speed is 0.71 v_max.
Each oscillates at twice the SHM frequency.
In more detail
In SHM, kinetic energy is ½mv² and potential energy is ½kx². Their sum is constant, with kinetic energy peaking at equilibrium and potential energy peaking at the extremes.
Real-world uses
- Engineering analysis of vibrating bridges and buildings uses energy balances.
- Physics labs track energy exchange using sensors on oscillating carts.
- Physicists plot kinetic and potential energy against time to see that they are out of phase by a quarter of a cycle.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Where is kinetic energy zero?
At the turning points, where the velocity is zero.
Where is potential energy zero?
At equilibrium, where displacement is zero.
Are the kinetic and potential energies ever equal?
Yes. They are equal at a displacement of A divided by the square root of two, where each is half the total energy.
Related topics in Oscillations & SHM
Second's pendulum · Simple pendulum in elevator · Energy in SHM · Average energy over a cycle · Differential equation of SHM · Damped oscillations