Simple harmonic motion and damped oscillationsEdexcel A-Level Further Maths: Flashcards

What these 13 flashcards ask

What is the equation for SHM?
General solution of \ddot{x}=-\omega^2x?
Amplitude when x=A\cos\omega t+B\sin\omega t?
Period and frequency of SHM?
Maximum speed and maximum acceleration in SHM?
For a mass m on a spring of stiffness k, what is \omega^2?
Standard form of the damped oscillator equation?
What happens in light damping?
What happens in critical damping?
What happens in heavy damping?
Which discriminant condition gives no oscillation for m^2+2\lambda m+\omega^2=0?
In a forced vibration, what is the transient?
In a forced vibration, what is the steady state?

Exam questions on Simple harmonic motion and damped oscillations

A particle moves on a straight line, with displacement $x$ metres from a fixed point $O$ at time $t$ seconds, so that $\ddot{x}=-16x$ . At $t=0$ the particle is at $x=0.5$ and is instantaneously at rest.
Find the displacement of the particle from $O$ when $t=\frac{\pi}{6}$ .2 marks
A damped oscillator has displacement $x$ at time $t$ satisfying $\ddot{x}+2c\dot{x}+25x=0$ , where $c>0$ is a constant.
Find the general solution of the differential equation when $c=3$ .2 marks
A particle of mass 2 kg lies on a smooth horizontal surface, attached to one end of a light spring of stiffness 50 N m $^{-1}$ . The other end of the spring is fixed. The spring is at its natural length when the particle is at $O$ , and $x$ metres is the displacement of the particle from $O$ at time $t$ seconds.
Show that $\ddot{x}+25x=0$ .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).