A \(0.400-\mathrm{kg}\) object is oscillating on a spring for which the force constant is \(300 \mathrm{~N} / \mathrm{m}\). A damping force that is linearly proportional to the object's velocity is exerted on the system, and the damping coefficient is \(b=5.00 \mathrm{~kg} / \mathrm{s}\).

(a) Verify that the units given for \(b\) are correct.

(b) What is the frequency \(f\) of the oscillation?

(c) What is the time constant \(\tau\) ? 

\((d)\) What is the quality factor \(Q\) ?