A2 June 2023 Paper 1 Q4

4 The solution of a second order differential equation is \(\mathrm{f}(t)\)

The differential equation models heavy damping.

Which one of the statements below could be true?

Tick (✓) one box. [1 mark]

• \(\mathrm{f}(t) = 2\mathrm{e}^{-t}\cos(3t) + 5\mathrm{e}^{-t}\sin(3t)\)
• \(\mathrm{f}(t) = 3\mathrm{e}^{-t} + 4t\mathrm{e}^{-t}\)
• \(\mathrm{f}(t) = 7\mathrm{e}^{-t} + 2\mathrm{e}^{-2t}\)
• \(\mathrm{f}(t) = 8\mathrm{e}^{-t}\cos(3t - 0.1)\)