SHM Velocity
Gives the velocity of a simple harmonic oscillator at any time t: v(t) = −Aω·sin(ωt + φ)
The equation
What it solves
Gives the velocity of a simple harmonic oscillator at any time t: v(t) = −Aω·sin(ωt + φ). It is the time derivative of x(t). Maximum speed Aω occurs at the equilibrium position.
When to use it
When you need instantaneous velocity at a given time, or the maximum speed (Aω) of the oscillation. Together with x(t), it fully describes the oscillator state.
When NOT to use it
Does not apply to damped or driven oscillators without modification. The sign convention (cosine for position, negative sine for velocity) is tied to the phase convention; verify consistency with your x(t) definition.
Common mistakes
Forgetting the negative sign — the velocity leads position by 90° but with a negative coefficient. Dropping the ω factor, which is the conversion between displacement amplitude A and velocity amplitude Aω. Confusing the speed |v| = Aω at equilibrium with the velocity v, which can be negative.