Damped oscillationsAQA A-Level Further Maths: Flashcards

What these 13 flashcards ask

Equation for damping proportional to velocity?
Standard form of a damped oscillation equation?
Condition for light damping?
Condition for critical damping?
Condition for heavy damping?
Solution for light damping?
Solution for critical damping?
Solution for heavy damping?
How does light damping affect the period?
What does critical damping achieve?
Roots of m^2+2m+10=0 and damping type?
What happens to x as t\to\infty in all three cases?
What does heavy damping look like?

Exam questions on Damped oscillations

A particle moves on a straight line, with displacement $x$ m from $O$ at time $t$ s, where $x''+6x'+25x=0$ .
Write down the general solution of the differential equation.2 marks
A particle of mass 0.5 kg moves on a straight line, with displacement $x$ m from $O$ at time $t$ s. It is acted on by a restoring force of magnitude $2|x|$ N towards $O$ and a resistive force of magnitude $\lambda v$ N, where $v$ m s $^{-1}$ is its speed and $\lambda$ is a positive constant.
State, with a reason, the type of damping when $\lambda=3$ .2 marks
The displacement $x$ m of a particle from $O$ at time $t$ s satisfies $x''+4x'+4x=0$ . When $t=0$ , $x=3$ and $x'=0$ .
Show that the damping is critical and write down the general solution.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).