Examples of sinusoidal in the following topics:



 For instance, when we studied the forced harmonic oscillator, we first solved the problem by assuming the forcing function was a sinusoid (or complex exponential).
 We then argued that since the equations were linear this was enough to let us build the solution for an arbitrary forcing function if only we could represent this forcing function as a sum of sinusoids.
 Later, when we derived the continuum limit of the coupled spring/mass system we saw that separation of variables led us to a solution, but only if we could somehow represent general initial conditions as a sum of sinusoids.

 But the second term may or may not be a sinusoid, depending on whether the square root is positive.
 First if $\frac{\gamma}{2\omega_0} < 1$ , corresponding to small damping, then the argument of the square root is positive and indeed we have a damped sinusoid.



 The extrema (peaks and troughs) of a sinusoid of frequency $f_s$ will lie exactly $1/2f_s$ apart.


