Question.5: In Figure, a cart of mass

M

carrying a simple pendulum with mass

m

and length

I

moves on a smooth horizontal surface. The cart is constrained by a viscous damper (

c

) and is subject to an external force

f

. For the pendulum to work, gravity

(g)

must be considered. For this two-DOF system, derive the independent governing equations of motion (Hints: 2 equations: one is

f

, and the other one is related to gravity without other external force). Also, obtain an expression of the tension (caused by gravity) of the pendulum cable (10 points).

Question.5: In Figure, a cart of mass M carrying a simple pendulum with mass m and length I moves on a smooth horizontal surface. The cart is constrained by a viscous damper ( c ) and is subject to an external force f. For the pendulum to work, gravity (g) must be considered. For this two-DOF system, derive the independent governing equations of motion (Hints: 2 equations: one is f, and the other one is related to gravity without other external force). Also, obtain an expression of the tension (caused by gravity) of the pendulum cable (10 points). Question.5: In Figure, a cart of mass M carrying a simple pendulum with mass m and length I moves on a smooth horizontal surface. The cart is constrained by a viscous damper ( c ) and is subject to an external force f. For the pendulum to work, gravity (g) must be considered. For this two-DOF system, derive the independent governing equations of motion (Hints: 2 equations: one is f, and the other one is related to gravity without other external force). Also, obtain an expression of the tension (caused by gravity) of the pendulum cable (10 points)