Quarter car suspension model The figure below a model of the suspension of a car. r(t)is the position of the mass of the car from its equilibrium position while z is the profile of the road. Note that z is a function of the distance y along the road, but you need (t) which you can obtain from z(y) using the chain rule. The car is traveling to the right on the road at a speed v. Assume the mass of the car is 250 kg, the spring constant is 16 kN/m, and damping constant is 1000 Ns/m. (a) Derive the differential equation for the position of the car r(t). (b) If z(t) Zoejwot, determine the amplitude and the phase of the particular solution. (c) (MATLAB) If the car is travelling with constant velocity along a road with rolling hills that can be represented as a cosine function with amplitude Zo and wavelength A (wavelength is the distance between adjacent crests or adjacent troughs, determine the vertical motion of the car as a function of time.

In the system, the two masses are equal and the cable neither stretches nor slips. The springs are undeflected when 0 = x1 = x2 = 0. M M Write down the equation of motion, and put it in state-variable (matrix) form.

T2 = ? T1 = ? M2 = 2 kg M1 = 5 kg M2 = 20 kg 1. Find the acceleration 2. Tension on the strings

C. Two masses are sliding along a rough surface as shown in the figure. The mass of each box is ma = mB = 10 kg. The masses are connected via a rope wrapped around a (frictionless, massless) pulley so that at the time shown the magnitude of the acceleration of each box is aA = AB = 0.5 m/s². KD: DO NOT SET-UP THE EQUATIONS OR SOLVE THE PROBLEM. KD: mB i. Your friend has chosen to use the rate form of the COLM to solve this problem. Neatly and completely label the system diagrams below to help your friend determine the coefficient of friction between the boxes and the rough surface. ii. List the unique unknowns in these diagrams: Block A 0 = 30° Block B FBD: pulley FBD: MA Block A 7 Block B