Determine the free-vibration response of the viscously damped systems described in Problem 2.149 when \(x_{0}=0.1 \mathrm{~m}\) and \(\dot{x}_{0}=10 \mathrm{~m} / \mathrm{s}\).

Data From Problem 2.149:-

Determine the values of \(\zeta\) and \(\omega_{d}\) for the following viscously damped systems:

a. \(m=10 \mathrm{~kg}, c=150 \mathrm{~N}-\mathrm{s} / \mathrm{m}, k=1000 \mathrm{~N} / \mathrm{m}\)

b. \(m=10 \mathrm{~kg}, c=200 \mathrm{~N}-\mathrm{s} / \mathrm{m}, k=1000 \mathrm{~N} / \mathrm{m}\)

c. \(m=10 \mathrm{~kg}, c=250 \mathrm{~N}-\mathrm{s} / \mathrm{m}, k=1000 \mathrm{~N} / \mathrm{m}\)