Answer:
see below
Step-by-step explanation:
We presume the damping constant is the opposite of the multiplier of time in the exponential term. Then the equations are ...
(a) y = a·e^(-ct)·sin(ωt)
(b) y = a·e^(-ct)·cos(ωt)
__
These are the standard equations for simple harmonic motion assuming there is no driving function.
a = initial amplitude*
c = damping constant**
ω = frequency of oscillation in radians per second
t = time in seconds
_____
* Of course, when y(0) = 0, the motion never actually reaches this amplitude because it is subject to decay before it can.
__
** In electrical engineering, damping is often specified in terms of a time constant, the time it takes for amplitude to decay to 1/e (≈36.8%) of the original amplitude. If that time is represented by τ, then the exponential factor is e^(-t/τ).
