(Solved): Figure 2: Pendulum System for problems 6-8 Consider the pendulum mechanism shown in Figu ...

Figure 2: Pendulum System for problems 6-8 Consider the pendulum mechanism shown in Figure 2, which pivots at point $\mathrm{O}$. Calculate both the damped and undamped natural frequency of the system for small angles. Assume that the mass of the rod, spring, and damper are negligible. Assume $F(t)=F\cos (?t)$. What driving frequency will cause resonance? Considering the same system in Figure 2, with $k=4000\mathrm{N}/\mathrm{m}.?1=0.05\mathrm{m},?2=0.07\mathrm{m}.?=0.10\mathrm{m}$. and $m=40\mathrm{kg}$. Design the dashpot (i.e. calculate c) so that the damping ratio of the system is 0.2 . Also determine the amplitude of vibration of the steady-state response if a $10?\mathrm{N}$ force is applied to the mass, as indicated in the figure, at a frequency of $10\mathrm{rad}/\mathrm{s}$.