Simple harmonic motionEdexcel A-Level Further Maths: Mind map

Exam questions on Simple harmonic motion

1. A particle $P$ moves in a straight line with simple harmonic motion about a fixed centre $O$. The amplitude of the motion is 0.8 m and the angular frequency is $\omega=5$ rad s⁻¹.
   Given that $x=0.8\sin5t$ with $t=0$ at $O$, find the time taken for $P$ to move directly from $O$ to a point 0.4 m from $O$.2 marks
2. A particle $P$ of mass 0.5 kg is attached to one end of a light elastic spring of natural length 0.4 m and modulus of elasticity 20 N. The other end of the spring is fixed to a ceiling and $P$ hangs in equilibrium. $P$ is then pulled vertically downwards a distance 0.05 m from the equilibrium position and released from rest. Take $g=9.8$ m s⁻².
   Find the maximum speed of $P$.2 marks
3. A particle $P$ of mass 0.4 kg lies on a smooth horizontal table. It is attached to two identical light elastic strings, each of natural length 0.8 m and modulus of elasticity 16 N. The other ends of the strings are fixed to points $A$ and $B$ on the table, where $AB=2.4$ m, and $P$ rests in equilibrium at the midpoint $M$ of $AB$. $P$ is then displaced along $AB$ and released from rest.
   $P$ is displaced a distance $x$ metres from $M$ towards $B$, with both strings taut. Show that $P$ moves with simple harmonic motion, and state the value of $\omega$.3 marks