- #1

danj303

- 15

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## Homework Statement

The suspension system of a car is designed so that it is a damped system described by

z'' + 2z' + z = f(t)

where z is the vertical displacement of the car from its rest position. The car is driven over a (smooth!) road which has "catseye" embedded in the road surface every

*d*metres. Assume that each time the car passes over a catseye, the suspension system receives a unit impulse. Thus, if the car is driven with velocity

*v m/s*over

*K + 1*catseyes then

f(t) = (see attachment)

(a) Find z(t) when z(0) = z'(0) = 0.

(b) Plot the solutions for K = 10 and K = 50 with v = 10 What is the effect of a larger K? Fix K = 50. Let v = 10 and plot the solutions for d = 5 and d = 10 on the same axes. What is the effect of the distance between the cateyes? Let d = 10 and plot the solutions for v = 10 and v = 20. What is the effect of speed?

## Homework Equations

on attachment