Question
L-mg
WW
CH
(?)
(a) Consider the wing of an aircraft as a mass spring system, show that the DE for the
system is
Mx" + cx' + kx = L(t) - Mg
Where L(t) is the lift or upward force
M is the mass of the wing
C is the viscous friction constant
K is the spring constant
(b) If L(t) = 3t, M = 1kg, g = 10m/s², C = 2Ns/m, k = 2N/m
Find a solution to the differential equation
The initial conditions are x(0) = 0 and x'(0) = 5
Question 2
The current voltage relationship for a diode is V = ln(3 + 4I)
Obtain a linear approximation for the voltage - current relationship when I = 1 A
Question 3
The table gives the values of a function obtained from an experiment with a thermistor
Temperature(K) 293
297
301
303
305
Resistance(?) 57.5
46.6
37.2
33.2
29.8
By first deriving the least squares equation, fit a 2<sup>nd</sup> order polynomial to the data
Question 4
A chemist has developed a fuel additive and claims that it reduces the fuel consumption of
cars. To test this claim, 8 randomly selected cars were each filled with 20 litres of fuel and
driven around a race circuit. Each car was tested twice, once with the additive and once
without. The distances, in miles, that each car travelled before running out of fuel are given in
the table below.
Car
1
2
3
4
5
6
7
8
Distance without additive 163 172 195 170 183 185 161 176
Distance with additive 168 185 187 172 180 189 172 175
Stating your hypotheses clearly test, at the 5% level of significance, whether or not there is
evidence to support the chemist's claim.
