## B27TA Computer Lab

EXERCISE 2: Car SuspensionSTART: WEEK 3 (week beginning 28th Sept)

TO BE MARKED BY: End of computer lab session in Week 4

Part 1:

Under certain circumstances, when sound travels from one medium to another, the fraction of

the incident energy that is transmitted across the interface is given by

E(r) = 4r /(r +1)2

where r is the ratio of the acoustic resonances of the two media. Sketch this function for r ³ 0

Without doing any calculations, quickly sketch the basic shapes of the following functions.

You may find these predictions useful for Exercise 3…

b = e-a2 b = ae-a2 2 ( ) 4

b = a2- 1 e-a

Part 2:

When a spring’s motion is damped – such as in a car where the shock absorbers contain

springs and either fluid or gas dampers – the motion of the end of the spring in response to a

shock is given by:

y(t) µ e-t t cos(wt) (2.1)

Where t is the damping time and the angular frequency, w, is related to the shock absorber

spring constant, k, as follows:

m

k w = (2.2)

Before going further, make a sketch below predicting what the basic functional form of

equation 2.1 should look like – discuss your prediction with a demonstrator before proceeding

further.

Now use Excel to investigate the function given by equation 2.1. Given that a typical value for

the damping time in a car (of mass 1000 kg) is around t = 0.25 s, suggest an appropriate

value for the spring constant of the shock absorber (start with a value of k = 50000 Nm-1 and

work from there). Justify your conclusions.

Would a heavier car require a stiffer spring?