Standard +0.3 This is a conceptual recognition question about damping types in differential equations. Students need to recall that heavy damping corresponds to two distinct real negative roots (no oscillation), making the third option correct. While it requires understanding of damping classifications, it's a single-mark multiple-choice question testing standard theory without calculation, making it slightly easier than average.
The solution of a second order differential equation is \(f(t)\)
The differential equation models heavy damping.
Which one of the statements below could be true?
Tick \((\checkmark)\) one box.
[1 mark]
\(f(t) = 2\mathrm{e}^{-t} \cos(3t) + 5\mathrm{e}^{-t} \sin(3t) \quad \square\)
\(f(t) = 3\mathrm{e}^{-t} + 4t\mathrm{e}^{-t} \quad \square\)
\(f(t) = 7\mathrm{e}^{-t} + 2\mathrm{e}^{-2t} \quad \square\)
\(f(t) = 8\mathrm{e}^{-t} \cos(3t - 0.1) \quad \square\)
The solution of a second order differential equation is $f(t)$
The differential equation models heavy damping.
Which one of the statements below could be true?
Tick $(\checkmark)$ one box.
[1 mark]
$f(t) = 2\mathrm{e}^{-t} \cos(3t) + 5\mathrm{e}^{-t} \sin(3t) \quad \square$
$f(t) = 3\mathrm{e}^{-t} + 4t\mathrm{e}^{-t} \quad \square$
$f(t) = 7\mathrm{e}^{-t} + 2\mathrm{e}^{-2t} \quad \square$
$f(t) = 8\mathrm{e}^{-t} \cos(3t - 0.1) \quad \square$
\hfill \mbox{\textit{AQA Further Paper 1 2023 Q4 [1]}}