The figure depicts Jack$-$in$-$the$-$box: "Jack" is attached inside a box by a spring, as shown. You estimate Jack's mass to be $0\mathrm{.}4kg.$ As so often happens, a sign tells you the spring constant: $k=166\frac{N}{m}.$ The Jack$-$in$-$the$-$box is immersed in a fluid. The fluid offers a resistive force $f=-bv,$ which damps the oscillation. Under the influence of this damping, you observe the period of the oscillation to be $0\mathrm{.}5s.$

a$)$ After one full oscillation, by what percentage does the amplitude decrease?

b$)$ In the same amount of time as one full oscillation, by what percentage does the total energy of the system decrease?