(Solved): i) For the single DOF mass-spring system shown in the figure below, determine the equivalent sp ...

i) For the single DOF mass-spring system shown in the figure below, determine the equivalent spring constant of the system. Assume ${\mathrm{k}}_1={\mathrm{k}}_2=3\mathrm{N}/\mathrm{m},{\mathrm{k}}_3={\mathrm{k}}_4=6\mathrm{N}/\mathrm{m}$, and ${\mathrm{k}}_5=7\mathrm{N}/\mathrm{m}$. [8 marks] Fig. Q6.a Answer: i) $K_{eq}=16[\mathrm{N}/\mathrm{m}]$ ii) In the mechanical system shown in Fig. Q.6.b, the link $OA$ is a uniform rigid bar, of mass $m$ and total length $l$, pivoted at point $O$, and supported by two linear springs both with the spring constant $k$. Assuming that the springs are unstretched and untwisted when the link is vertical, a) Derive the equation of motion of the system for small angular displacements. [9 marks] b) Determine the natural frequency of the system $\left({?}_n\right)$. [3 marks] [Total: 20 marks]