Simple harmonic motionEdexcel International A Level Further Maths: Mind map

Exam questions on Simple harmonic motion

1. A particle moves in a straight line with simple harmonic motion about a centre $O$. The amplitude of the motion is $0.5$ m and the period is $2$ s.
   Find the speed of the particle when it is $0.3$ m from $O$.2 marks
2. The displacement of a particle $P$ from a fixed point $O$ on a straight line, at time $t$ seconds, is $x=0.4\cos3t$ metres.
   Find the first time at which $P$ is at $x=-0.2$ m.2 marks
3. A particle $P$ of mass $2$ kg moves on a smooth horizontal straight line. When $P$ is at displacement $x$ metres from a fixed point $O$ on the line, the only horizontal force on $P$ is directed towards $O$ and has magnitude $18x$ N.
   Show that $P$ moves with simple harmonic motion, and find the period of the motion.3 marks