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 Q$3.$ The trolley has a pendulum of length l with bob mass

$($M$)$ attached. Assume the wheels of the trolley and the pendulum string are massless.

$($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.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 Q$3.$ 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.

$($a$)$ Find the equations of motion for free oscillation. Do not assume small angles of $.$

$($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.