Question

Choose and state a vehicle from the assigned class above. Next, to construct your mathematical model, you may assume that the mass of the vehicle is distributed evenly throughout the car (for simplicity). Here, m (in kg) will represent the mass of the vehicle, the dampener attached to the suspension will have a damping coefficient of c (in N/(m/s)), and the spring constant, otherwise known as the spring rate, of the coil in the suspension application will be k (in N/m). Without an external force acting on the suspension, the second order differential equation governing this system is given below.
Mass is 1205 kg

m/4y''+ cy'+ky=0

Enter in your value for the mass, converted into kg.

Spring constant for mini cooper S = 28.25 N/m

Write this second order differential equation as a first order matrix-vector system of differential equations. Show your work in detail.

Now, suppose the front left portion of your vehicle drifts off a curb of height 0.15 meters without an initial velocity. Write an appropriate initial condition using proper notation describing this event and pair it with your first order system.

Answer 1

To convert a second-order differential equation into a system of linear differential equation, we have to write y'' as x', for some variable x.