A horizontal spring mass system is to be constructed. A spring which has a spring constant of $0\mathrm{.}5$ kg$/$s will be used. The system should be designed so that when it is released and vibrating freely $($there is no forcing$)$ the amplitude of its vibrations will decay like e$^(-0\mathrm{.}5$t$),$ and it should oscillate with a period of $4\mathrm{.}5$ seconds.

$($Although the motion is oscillatory it is not strictly periodic because the amplitude decays exponentially. In this context "period" refers to the period of the sine and$/$or cosine functions that create the oscillations in the motion.$)$

Based on these constraints determine the mass of the object, M$($kg$),$ to be used, and also determine the value of the friction coefficient, b$($kg$/$s$).$