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

Exam questions on Simple harmonic motion and damped oscillations

1. 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
2. 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
3. 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