Chapter 27, Problem 21P

The following differential equation can be used to analyze the vibrations of an automobile shock absorber:

$1.25\times {10}^6\frac{d^{2}x}{d{t}^2}+1\times {10}^7\frac{dx}{dt}+1.5\times {10}^{9}x=0$

Transform this equation into a pair of ODEs. (a) Use MATLAB to solve these equations from t 5 0 to 0.4 for the case where $dx/dt=0\text{ at }t=0$. (b) Use MATLAB to determine the eigenvalues and eigenvectors for the system.