Find the variation of the displacement with time, \(x(t)\), of a damped single-degree-of-freedom system with \(\zeta=2.0\) for the following initial conditions:

a. \(x(t=0)=x_{0}=0.2 \mathrm{~m}, \dot{x}_{0}=0\)

b. \(x(t=0)=x_{0}=-0.2 \mathrm{~m}, \dot{x}_{0}=0\)

c. \(\dot{x}_{0}=0.2 \mathrm{~m} / \mathrm{s}, x_{0}=0\)

d. Plot the variations of displacement found in parts (a), (b), and

(c) on the same graph in the range of 0 to \(5 \mathrm{~s}\).