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Question 10 (Thomson 2-41) Set up the different ial equaiton of motion fo rht eysstme shown in Fig-Q10. Determine the expression for (a) The critical damping coefficient, (b) And the natural frequency of damped oscillation (Damped natural frequency) ANS: $(a) c_{c}=\frac{2 m l}{a} \sqrt{\frac{k}{m}}$, (b) $\omega_{d}=\frac{a}{l} \sqrt{\frac{k}{m}} \sqrt{1-\left(\frac{a c}{2 m l}\right)^{2} \frac{m}{k}}$ Fig-Q10: A example of dynamic system.

Set up the differential equation of motion for the system shown. Determine the expression for a.) critibal damping coefficient and b.) the natural frequency of damped oscillation (damped natural frequency)

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