Question

x(t) y(d) Consider the spring-mass-damper system above travelling along a bumpy surface with a height change. The damping ratio is =0.2, the natural frequency is 3 rad/s, and the mass, m=200 kg. The wheel does not lose contact with the road and the road has the shape, y(d)4sin 0H(d 10) where d is distance in meters, and y(d) is the height in centimeters 1. Write the ordinary differential equation for v-1 m/s and v-5 m/s. 2. The solution of x(t) is a combination of the homogeneous response, rH (t), forced sinusoidal response Zpí (t), and forced step response Zp2(t). Solve for the homogeneous and forced response, a(t) = 패+1P1 for the base excitation for d<10 m. For v-1 and 5 m/s 3. Solve for the step response of the system, xp2(t) using x(d-10)(d-10)-0. For v-1 and 5 m/s. Hint: The base ercitation will be a combination of a Heaviside (H(t - d/v)) and dirac delta, ( - d/v)).

Answer 1

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