Edexcel M3 2014 June — Question 1 8 marks

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
Year2014
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimple Harmonic Motion
TypeFind amplitude of SHM
DifficultyStandard +0.3 This is a standard SHM question requiring application of standard formulas (ω = 2π/T, a = -ω²x, v_max = ωa) with straightforward substitution. Part (c) requires slightly more thought about distance traveled, but follows a routine approach for M3 level, making it slightly above average difficulty.
Spec4.10f Simple harmonic motion: x'' = -omega^2 x4.10g Damped oscillations: model and interpret

  1. A particle \(P\) moves in a straight line with simple harmonic motion. The period of the motion is \(\frac { \pi } { 4 }\) seconds. At time \(t = 0 , P\) is at rest at the point \(A\) and the acceleration of \(P\) has magnitude \(20 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
Find
  1. the amplitude of the motion,
  2. the greatest speed of \(P\) during the motion,
  3. the time \(P\) takes to travel a total distance of 1.5 m after it has first left \(A\).

\begin{enumerate}
  \item A particle $P$ moves in a straight line with simple harmonic motion. The period of the motion is $\frac { \pi } { 4 }$ seconds. At time $t = 0 , P$ is at rest at the point $A$ and the acceleration of $P$ has magnitude $20 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\end{enumerate}

Find\\
(a) the amplitude of the motion,\\
(b) the greatest speed of $P$ during the motion,\\
(c) the time $P$ takes to travel a total distance of 1.5 m after it has first left $A$.\\

\hfill \mbox{\textit{Edexcel M3 2014 Q1 [8]}}