Simple harmonic motionAQA A-Level Further Maths: Mind map

Exam questions on Simple harmonic motion

1. A particle moves on a straight line with displacement $x$ m from a fixed point $O$ at time $t$ s, where $x''=-16x$. When $t=0$, $x=0.3$ and the particle is at rest.
   Find an expression for $x$ in terms of $t$.2 marks
2. A particle moves with simple harmonic motion about a fixed point $O$, with period 2 s and amplitude 0.5 m.
   Find the speed of the particle when it is 0.3 m from $O$.2 marks
3. A particle of mass 2 kg hangs in equilibrium from a fixed point on a light vertical spring, where the tension is $T=kx$, with $x$ m the extension and $k=200$ N m$^{-1}$. The particle is pulled a further 0.05 m downwards and released from rest at $t=0$. Let $y$ m be the displacement of the particle below its equilibrium position at time $t$ s. Assume the spring stays taut.
   Show that $y''=-100y$.3 marks