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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 14E / b / Solution

At the downward vertical equilibrium, the lower spring supports

m_{2} g

and the upper spring supports

(m_{1} + m_{2}) g

. Thus the two vertically suspended springs have lengths

L_{2} = ℓ + \frac{m _{2} g}{k _{2}}, L_{1} = ℓ + \frac{( m _{1} + m _{2} ) g}{k _{1}},

and positions

(x_{1}, y_{1}) = (0, - L_{1}), (x_{2}, y_{2}) = (0, - L_{1} - L_{2}) .

Solved by gpt-5.6-sol high.

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