Question

You are designing a suspension system for a 1000 kg automobile whose acceleration can be described by the following equation: a( ?x, x) = ?(c/m) ?x?(k/m)x (m/s2 ) where c is the damping constant for the shock absorber and k is the spring constant. The initial conditions are: v(0) = 0 and x(0) = 0.01 m. k = 400 kN/m. Note: You will want to use The Runge-Kutta Method to numerically solve the equation. You can use the functions provided in MATLAB and Python to do this. As part of your design, do the following:

1. Solve the differential equation by hand

. 2. Choose a value for c such that the oscillations will damp out after two cycles.

3. Plot the acceleration (m/s2 ) vs time (s).

4. Plot the velocity(m/s) vs time (s).

5. Plot the position (m/s) vs time (s).

Answer 1