A mass-damper-spring system has equation of Ax + Bx + Cx = D (A in kg, B i n Ns/m,C in N/cm and D is external force in Newton). 1- Calculate the natural frequency and damping ratio of the system? 2- Describe the type of this vibrational system based on its damping ratio? 3- If we want to have a critical damped case, find the corresponding spring constant C. 4- If we would like to double the damping ratio, how much we should change mass A? 5- Clearly describe the resonance phenomena in excited mechanical vibration systems in your own wordings? (8 pts) 6- Explain in detail if there is a way in the current example that by changing force D, we can create resonance? If yes, what value of force D results resonance? (10 pts)

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A mass-damper-spring system has equation of Ax + Bx + Cx = D (A in kg, B i n Ns/m,C in N/cm and D is external force in Newton). 1- Calculate the natural frequency and damping ratio of the system? 2- Describe the type of this vibrational system based on its damping ratio? 3- If we want to have a critical damped cas