Past exam of the mathematics course of the University of Cambridge / 2019 / ia / Paper 2 / 7C / c

Table of contents
- Solution c

Solution

For

t > 2

, the Heaviside step function contributes a constant unit forcing. Solving the resulting first-order linear differential equation from the value at

t = 2

gives

T_{1} (t) = T_{\infty} + (Δ - e^{a}) e^{- a t} + \frac{1}{a} (1 - e^{- a (t - 2)}) .

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