Formula Undamped Harmonic Oscillator Velocity Current position Mass Spring constant Amplitude
$$v(x) ~=~ \sqrt{ \frac{D}{m} \, \left(A^2 - x^2\right) }$$ $$v(x) ~=~ \sqrt{ \frac{D}{m} \, \left(A^2 - x^2\right) }$$
Velocity
$$ v $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$ Velocity \(v(x)\) of an undamped harmonic oscillator as a function of its current position \(x\). For example, its velocity is zero at the maximum deflection \(A\):$$ v(A) ~=~ \sqrt{ \frac{D}{m} \, \left(A^2 - A^2\right) } ~=~ 0 $$
Current position
$$ x $$ Unit $$ \mathrm{m} $$ Current position of a harmonic oscillator at which it has the velocity \(v(x)\). For example, it could be the current deflection of the spring on which a mass is attached.
Mass
$$ m $$ Unit $$ \mathrm{kg} $$ Mass of the harmonic oscillator. For a spring pendulum, it is in good approximation the mass hanging on the spring. In the case of a spring whose mass cannot be neglected, a part of the mass of the spring must also be taken into account in \(m\) because it also oscillates.
Spring constant
$$ D $$ Unit $$ \frac{\mathrm N}{\mathrm m} $$ Spring constant describes the stiffness of a spring, i.e. how well the spring can be deflected.
Amplitude
$$ A $$ Unit $$ \mathrm{m} $$ Maximum deflection of a harmonic oscillator. In the case of a spring pendulum, it is the maximum distance of the mass from the rest position (undeflected mass).