Consider this forced translational mass$-$spring$-$damper $($MSD$)$ system:

The input is the external force $"F(t)"$ and the output is position $"x(t)."$

The transfer function for this system is

$G(s)=\frac{x((s))}{F((s))}=\frac{1}{M{s}^2+Bs+K}$

It is known that $M=1kg,B=8\frac{(N)}{\frac{m}{sec}},$ and there are three possible values of K :

$(K_1=15\frac{(N)}{(m)},K_2=20\frac{(N)}{(m)},K_3=41\frac{(N)}{(m)})$

The only possible external forces $"F(t)"$ have the following Laplace transforms:

$F_1(s)=\frac{70(s)}{s^2+49}($corresponding to external force $"f_1(t)")$

$F_2(s)=\frac{21}{(s)+8}($corresponding to external force $"f_2(t)")$

$F_3(s)=\frac{12}{(s)}($corresponding to external force $"f_3(t)")$