Simple harmonic motionAQA A-Level Further Maths: Flashcards

What these 13 flashcards ask

State the equation for simple harmonic motion.
What does the minus sign in x''=-\omega^2x show?
General solution of x''=-\omega^2x?
Period of SHM in terms of \omega?
Amplitude of x=A\cos\omega t+B\sin\omega t?
Formula for the speed at displacement x?
Where is the speed greatest, and what is it?
Where is the acceleration greatest, and what is it?
Hooke's law?
Mass m on a spring of constant k: value of \omega^2?
Why is a vertical spring still SHM?
Released from rest at displacement a: what is x?
x''=-25x: find the period.

Exam questions on Simple harmonic motion

A particle moves on a straight line with displacement $x$ m from a fixed point $O$ at time $t$ s, where $x''=-16x$ . When $t=0$ , $x=0.3$ and the particle is at rest.
Find an expression for $x$ in terms of $t$ .2 marks
A particle moves with simple harmonic motion about a fixed point $O$ , with period 2 s and amplitude 0.5 m.
Find the speed of the particle when it is 0.3 m from $O$ .2 marks
A particle of mass 2 kg hangs in equilibrium from a fixed point on a light vertical spring, where the tension is $T=kx$ , with $x$ m the extension and $k=200$ N m $^{-1}$ . The particle is pulled a further 0.05 m downwards and released from rest at $t=0$ . Let $y$ m be the displacement of the particle below its equilibrium position at time $t$ s. Assume the spring stays taut.
Show that $y''=-100y$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).