 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2013/8/a/solution

With angles measured from the downward vertical, the upper mass rises by

2 l (1 - cos θ_{1})

and the lower by

2 l (1 - cos θ_{1}) + l (1 - cos θ_{2})

. Taking zero gravitational potential energy at the hanging equilibrium therefore gives the exact result

U = m g l [4 (1 - cos θ_{1}) + (1 - cos θ_{2})] .

Both masses contribute to the elevation change caused by the upper rod.

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