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Engineering interview
Model real problems, estimate scale and explain trade-offs.
One thinking framework
Use the same five steps for the exercises below. Familiarise yourself once, then focus on explaining your reasoning.
Five steps for your reasoning
1
Define variables, assumptions and a model
State what you are studying and what you will temporarily ignore.
2
Explain your choice of method
Connect your formula, theorem or comparison to the problem.
3
Explain each step as you calculate
Explain relationships, substitutions and intermediate conclusions.
4
Check units, scale and plausibility
Check signs, ranges, dimensions and possible sources of error.
5
Adapt to hints and changes
Identify which assumption changes and revise your approach.
1
A small ball of mass m is hung vertically by a spring of stiffness k, pulled down a certain distance from the equilibrium position and then released. (a) Starting from the forces, derive the differential equation of its motion; (b) hence show that it undergoes simple harmonic motion, and find the period; (c) if the whole apparatus is placed in a freely falling lift, how would the motion change?
2
When a sausage is put in the pan to cook, the skin almost always splits along the 'length direction' rather than around a 'ring'. Why?
3
In a plane flying high in clear skies (about 11 km above the ground), what is the approximate distance from you to the horizon at sea level? (Take the Earth's radius as 6400 km)
4
A capacitor C discharges through a resistor R. (a) Write down the circuit voltage equation and derive the differential equation for the charge Q as a function of time; (b) solve for Q(t); (c) define the time constant and sketch the current–time curve.
5
An electric vehicle of total mass M travels on a straight level road at constant power P. Ignore rolling resistance and consider only air resistance proportional to the square of the speed (F=kv²). Find the maximum speed it can reach, and explain why its acceleration becomes progressively smaller.
6
Why were the chimneys of old mills built so tall? Give as many independent reasons as you can from engineering principles.