A single degree of freedom spring-mass-damper system which is initially at rest at its equilibrium position is excited by an impulsive force over a time interval of \(1.5 \mathrm{~ms}\); see Fig. P3.6. If the mass is \(2 \mathrm{~kg}\), the stiffness is \(1 \times 10^{6} \mathrm{~N} / \mathrm{m}\), and the viscous damping coefficient is \(10 \mathrm{~N}-\mathrm{s} / \mathrm{m}\), complete the following.

Fig. P3.6 Spring-massdamper system excited by an impulsive force

(a) Determine the maximum allowable force magnitude if the maximum deflection is to be \(1 \mathrm{~mm}\).
(b) Plot the impulse response function, \(h(t)\), for this system. Use a time step size of \(0.001 \mathrm{~s}\).
(c) Calculate the impulse of the force \((\mathrm{N}-\mathrm{s})\).

k C x(t) m f(t)