For an object undergoing simple harmonic motion, this equation gives the velocity of the object as a function of time.

v is the velocity of the object

v_{max}is a constant. It is the maximum velocity of the object.

f is the frequency of oscillations.

t is the time.

**Note:** v_{max} **does**
depend on the frequency and amplitude of the oscillations (see
"v_{max} = 2 pi f" on formula sheet). We
call v_{max} a **constant** because
once the object undergoing simple harmonic motion is set into
motion, v_{max} does not change.

**Tip:** It is typically easier to find the
velocity of the object at a specified position using conservation
of energy than it is using this equation.

**Pitfall Avoidance Note**: The
v in this equation is **not wave velocity**. This v
is the velocity of an object undergoing simple harmonic motion.
To be sure, although this v was introduced in the simple harmonic
motion part of the physics course, not the wave part, it does
have something to do with wave motion. Consider a vertical wave
in a horizontal string. Each point on the string undergoes simple
harmonic motion. Each point goes up and down while the wave
itself travels along the length of the string. Pick any point
along the length of the string. The simple harmonic motion
equations apply to that point. The frequency of the wave and the
amplitude of the wave are the frequency of the oscillations and
the amplitude of oscillations of that point. But the speed of
that point is **not** the speed of the wave. How
fast that point is going upward, as a function of time, is indeed
given by the equation on this page. The speed of the wave
however, how fast the pattern moves forward along the length of
the string, is given by the equation v = lambda / T where lambda is the wavelength of the wave, a
characteristic not possessed by a simple harmonic oscillator.