(Solved): Consider the single degree of freedom system shown in figure 2 (damped oscillation) Figure 2 a) Sh ...

Consider the single degree of freedom system shown in figure 2 (damped oscillation) Figure 2 a) Show that \( \ddot{x}=-\frac{c}{m} \dot{x}-\frac{k}{m} x \). Hence plot the displacement (x) and velocity (dx/dt) for four cycles where \( \zeta=0.1, m=1 \mathrm{~kg} \) and \( k=100 \mathrm{~N} / \mathrm{m} \), given the initial conditions \( x(0)=0.02 \mathrm{~m} \) and \( \dot{x}(0)=0 \mathrm{~m} / \mathrm{s} \). 20 marks b) Replot the displacement \( (x) \) and velocity (dx/dt) for four cycles for \( k=200 \mathrm{~N} / \mathrm{m} \) and comment on the differences from the plots where \( k=100 \mathrm{~N} / \mathrm{m} \). 20 marks