Let's model this situation with a 2ad order ODE. Recall that the governing equation for a mass-spring-damper is given by the following. Where m is the mass of the tire, b is the damping constant, and k is the spring constant. Let's assume these values for m = 15, k = 2564, and b = 144. We wish to perform a bounce test to see if our shock absorbers are still in good condition.

#1: Solve for the general solution of the differential equation. Use your calculator to compute the roots in decimals instead of the fractions.

#2: We can model a bounce test by setting the initial displacement equal to 20 (i.e. (0) = 20). Assume that the system starts from rest (i.e. x'(0) = 0). Solve the initial value problem.

CoursHeroTranscribedText

dx dx m +b+kx=0 dt dt