An electromechanical system is shown in Fig. P 9.11. On energising the solenoid with \(e(t)\), the lower arm of lever \(\mathrm{P}\) moves to the left and upper arm to the right. The coil has resistance \(\mathrm{R}\) and inductance L. The solenoid pull \(\mathrm{F}=\mathrm{K} i(t)\) where \(i(t)\) is current through solenoid. Obtain transfer function model \(\mathrm{X}(s) / \mathrm{E}(s)\) of the system. Ignore all inertia and consider effects of spring \(\mathrm{K}\) and viscous damper B only. The back emf constant is \(\mathrm{K}_{b}\). The displacement of upper arm is \(x\).

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