Consider a spring-mass system, with \(k=4000 \mathrm{~N} / \mathrm{m}\) and \(m=10 \mathrm{~kg}\), subject to a harmonic force \(F(t)=400 \cos 20 t \mathrm{~N}\). Find and plot the total response of the system under the following initial conditions:

a. \(x_{0}=0.1 \mathrm{~m}, \dot{x}_{0}=0\)

b. \(x_{0}=0, \dot{x}_{0}=10 \mathrm{~m} / \mathrm{s}\)

c. \(x_{0}=0.1 \mathrm{~m}, \dot{x}_{0}=10 \mathrm{~m} / \mathrm{s}\)