A single degree of freedom spring-mass-damper system which is initially at rest at its equilibrium position is excited by an impulsive force with a magnitude of \(250 \mathrm{~N}\) over a time interval of \(0.5 \mathrm{~ms}\); see Fig. P7.8. If the mass is \(3 \mathrm{~kg}\), the stiffness is \(3 \times 10^{6} \mathrm{~N} / \mathrm{m}\), and the viscous damping coefficient is \(120 \mathrm{~N}-\mathrm{s} / \mathrm{m}\), complete the following.

Fig. P7.8 Spring-mass-damper system excited by an impulsive force.

(a) Determine \(x(t)\) using Eq. 3.44. Plot the response (in \(\mu \mathrm{m}\) ) over a time period of \(0.3 \mathrm{~s}\) with a step size of \(1 \times 10^{-4} \mathrm{~s}\) in the time vector.
(b) Determine \(x(t)\) using Euler integration. Use a time step of \(1 \times 10^{-4} \mathrm{~s}\) and carry out your simulation for \(0.3 \mathrm{~s}\) ( 30,000 points). Plot \(x(t)\) (in \(\mu \mathrm{m}\) ) versus time.

Transcribed Image Text:

k C 250- (N) x(t) m f(t) 0.5x10 3 1(s)