Candidates should answer BOTH compulsory questions.
Time Allowed: 1 hour.
Only calculators that conform to the list of models approved by the School of Engineering
may be used in this examination. The Engineering Data Book and standard graph paper
will be provided.
Read carefully the instructions on the answer book and make sure that the particulars required
are entered on each answer book.
, ES1970
1. a. Figure 1.1 shows a system diagram for a hot water tank which has capacitance and
is at temperature . The tank is insulated from the surroundings by a thermal resistor with
resistance R and the rate of heat flow from the tank to the surroundings is ( ).
Derive the input-output equation for the system in Figure 1.1, where the output is the
temperature of the tank and the inputs are the ambient temperature and rate of heat
flow into the tank ( ). Give TWO assumptions that would be made when considering
this tank as a lumped system. (5 marks)
Figure 1.1
b. Figure 1.2 shows a mechanical system with a mass M that is connected to a fixed
surface via a damper with co-efficient B1 and a spring with stiffness K. There is viscous
friction with co-efficient B2 between the mass and a fixed surface. The displacement of
the mass is x(t) and the input force to the mass is f(t). Draw a labelled free-body
diagram for the system. (5 marks)
Figure 1.2
Question 1 Continued Overleaf
2
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