Answer Happy

NEED THIS IN A WOLFRAM MATHEMATICA µb FILE. PLEASE READ ALL INSTRUCTIONS AND COMMENT EVERY STEP TO UNDERSTAND WHAT YOU DO. THANK YOU!!! Questions to be answered 1. Derive mathematical model of the suspension system (LCCDE). 2. Determine the system transfer function (H(s)). 3. Simulate the response of the given suspension system y(t) (car displacement) when the car moves over each of the three specified pavements x(t). Pavement profile Suppose that the object (car) moves in x-direction with constant velocity. It will experience a displacement in y-direction depending on the pavement conditions (Figure 1) and the properties of the suspension system. Curb A₁ Pothole 0 Pavement Figure 1. Pavement profiles Pavement is characterized by the following parameters: •x(t)- input, vertical displacement of the pavement, defined relative to a reference ground level (road profile). *y(t)-output, vertical displacement of the car chassis from its equilibrium position. 4. Formulate criteria for the suspension system optimization. How the suspension system parameters (k, b) can be modified to optimize the suspension system performance. Project Problem Statement This project is based on the analysis of second order LCCDE given in the textbook Chapter 2, "Linear Time-Invariant Systems". Special attention should be paid to the following items: 1. Impulse response of second order LCCDEs 2. Step response of second order LCCDEs 3. Sinusoidal response of second order LCCDEs Quarter-car suspension system parameters - Set 1 m =250 kg - suspended body mass (one fourth of the car's total mass, because the car has four wheels). k=10000 N/m-spring constant of the suspension system. b=4000 sN/m-damping coefficient of the shock absorber. A1 -0.1 m-curb height. A2 -0.1 m - pothole depth. A3 -0.1 m-wavy (sinusoidal)pavement amplitude. T=1.5 s-wavy (sinusoidal)pavement period. Suspension system model The simplified suspension system model is basically a mass-spring-damper system with suspended body mass, the suspension coil as the spring, and the shock absorber as the damper (Figure 2). This suspension system is characterized by the following parameters: • m- suspended body mass (kg) - one-fourth of the car's total mass, because the car has four wheels • k-spring constant (or stiffness of the coil) of the suspension system (N/m) • 6-damping coefficient of the shock absorber (N-s/m) y(1) Fo CAR Mass m Coil with spring constant k Shock absorber Fd with damping F₁ coefficient b x(1) TIRES Pavement Figure 2. Car suspension system model schematic