Q1: Consider the four-wheeled cart with a spring and damper as shown. Assume that the wheels...

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Q1: Consider the four-wheeled cart with a spring and damper as shown. Assume that the wheels are solid disks rolling without slip; each wheel has a mass m and a radius r, the cart has a mass M and the spring has a stiffness k and a mass m,, the viscous damper has a damping coefficient denoted by c. If M-8 kg, k =1500 N/m, m, -3 kg, m=1 kg, r=0.2 m, c= 150 N.s/m. a) Determine meq, keq, and ceq at x b) Write down the equation of motion for the system c) Determine the damping ratio and natural frequency d) Determine the response x(t) for the initial conditions: * = 0.1m, x=0. e) If a harmonic external force F(t) 150 sin(5t) [N] is applied at the mass M in the direction of x-axis, determine the steady state response x(t). f) Based on the result obtained in part e, determine the magnitude of the force exerted on the wall through the spring k. g) What should be the value of c to produce a critically damped system. k.m M w Q1: Consider the four-wheeled cart with a spring and damper as shown. Assume that the wheels are solid disks rolling without slip; each wheel has a mass m and a radius r, the cart has a mass M and the spring has a stiffness k and a mass m,, the viscous damper has a damping coefficient denoted by c. If M-8 kg, k =1500 N/m, m, -3 kg, m=1 kg, r=0.2 m, c= 150 N.s/m. a) Determine meq, keq, and ceq at x b) Write down the equation of motion for the system c) Determine the damping ratio and natural frequency d) Determine the response x(t) for the initial conditions: * = 0.1m, x=0. e) If a harmonic external force F(t) 150 sin(5t) [N] is applied at the mass M in the direction of x-axis, determine the steady state response x(t). f) Based on the result obtained in part e, determine the magnitude of the force exerted on the wall through the spring k. g) What should be the value of c to produce a critically damped system. k.m M w