A horizontal spring mass system is to be constructed. A spring which has a spring constant of 1 kg/s${}^2$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 $e^{-0.2 t}$, and it should oscillate with a period of 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).

$M$: kg
$b$: kg/s