SHM velocity

Intermediate

Velocity leads displacement by 90°.

Key relationv = −Aω sin(ωt+φ)

v = −Aω sin(ωt + φ), maximum Aω at the equilibrium and zero at the extremes. Also v = ω√(A² − x²).

Worked example

A = 0.1 m, ω = 10: v_max = 1 m/s.

Common mistake

Velocity peaks when the displacement is zero.

In more detail

The velocity in SHM is v(t) = −Aω sin(ωt + φ), which is greatest at equilibrium and zero at the turning points.

Speedometers in pendulum clocks show the maximum speed at the lowest point.
Analysing how fast a mass passes its equilibrium on a spring.
A sensor measuring the velocity of a vibrating tuning fork finds the peak velocity occurs when the fork passes through its centre.

Where is the speed maximum?

At the equilibrium position, where displacement is zero.

What is the maximum speed?

Aω, where A is the amplitude and ω is the angular frequency.

Where is the speed highest in SHM?

At the equilibrium position, where the displacement is zero and the kinetic energy is at its greatest.