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(II) USING THE LAPLACE TRANSFORM TO SOLVE DIFFERENTIAL EQUATIONS PROBLEM 1: (A practical example with repeated poles) A car of mass M and friction coefficient Kris stopped at a red traffic light (initial position and initial speed are zero). At 1-0, when the light turns green, a unit-step input force u(t) is applied to the car. In this problem, we are interested in the car position(0); not the car speed. (30 points) Find the car transfer function Y(s)y U(s). Find the car position y(0) as a function of time, in terms of the car parameters M a (10 points) Plot this step response for M K. nd Kf. Hint # 1 : when considering position (rather than speed, Newtons law becomes: Total of 130 points-100 %

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