Moderate -0.8 This is a standard SHM recognition question requiring only recall of the formula relating ω² to the coefficient in d²x/dt² = -ω²x, then applying T = 2π/ω. It's a 1-mark multiple choice question testing direct formula application with no problem-solving or derivation required, making it easier than average even for Further Maths.
The displacement of a particle from its equilibrium position is \(x\) metres at time \(t\) seconds.
The motion of the particle obeys the differential equation
$$\frac{d^2x}{dt^2} = -9x$$
Calculate the period of its motion in seconds.
Circle your answer.
[1 mark]
\(\frac{\pi}{9}\) \(\quad\) \(\frac{2\pi}{9}\) \(\quad\) \(\frac{\pi}{3}\) \(\quad\) \(\frac{2\pi}{3}\)
The displacement of a particle from its equilibrium position is $x$ metres at time $t$ seconds.
The motion of the particle obeys the differential equation
$$\frac{d^2x}{dt^2} = -9x$$
Calculate the period of its motion in seconds.
Circle your answer.
[1 mark]
$\frac{\pi}{9}$ $\quad$ $\frac{2\pi}{9}$ $\quad$ $\frac{\pi}{3}$ $\quad$ $\frac{2\pi}{3}$
\hfill \mbox{\textit{AQA Further Paper 1 2022 Q1 [1]}}