A horizontal oscillator has a massless spring with constant $k=100\frac{N}{m}$ attached to a mass of $1$ kg $.$ The spring is stretched to $3\mathrm{.}00$ m and held stationary before being released. The oscillator is damped with a linear medium such that the oscillation's amplitude decays to approximately $13\mathrm{.}53352832\%$ of its original value after $1$ second.

a$.$ Given that the system is NOT overdamped, find the decay parameter.

b$.$ Write the position and velocity equation for the oscillator.

c$.$ What is the maximum velocity $($magnitude$)$ of this oscillator?

d$.$ If we add a driving force of $(5N)cos(wt)$ where $w=6ra\frac{d}{s}$ to this oscillator, find the position equation for this oscillator.