Damped oscillationsAQA A-Level Further Maths: Mind map

Exam questions on Damped oscillations

1. 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
2. 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
3. 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