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:
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
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?

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