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A trolley of mass M is attached to ground via a spring of stiffness k and a damper of constant c as shown in

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A trolley of mass M is attached to ground via a spring of stiffness k and a damper of constant c as shown in Figure Q3. The trolley has a pendulum of length I with bob mass (M) attached. Assume the wheels of the trolley and the pendulum string are massless. Figure Q3 www The M -X (a) Find the equations of motion for free oscillation. Do not assume small angles of 0. (b) Find the equations of motion assuming small angles and place these in matrix form. Comment on the linearity of the equations when small angles are assumed.

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