Standard +0.3 This is a straightforward SHM question requiring standard formulas (x = a cos(ωt), period relation) and basic algebraic manipulation. Students must find ω from the period, recognize the initial conditions place P at maximum displacement, then solve for t when displacement is 0.25 - 0.375 = -0.125 m. While it requires careful setup and solving a trigonometric equation, it involves only routine SHM techniques with no novel insight needed, making it slightly easier than average.
A particle \(P\) moves in a straight line with simple harmonic motion about a fixed centre \(O\) with period 2 s. At time \(t\) seconds the speed of \(P\) is \(v\) m s\(^{-1}\). When \(t = 0\), \(v = 0\) and \(P\) is at a point \(A\) where \(OA = 0.25\) m.
Find the smallest positive value of \(t\) for which \(AP = 0.375\) m.
[6]
A particle $P$ moves in a straight line with simple harmonic motion about a fixed centre $O$ with period 2 s. At time $t$ seconds the speed of $P$ is $v$ m s$^{-1}$. When $t = 0$, $v = 0$ and $P$ is at a point $A$ where $OA = 0.25$ m.
Find the smallest positive value of $t$ for which $AP = 0.375$ m.
[6]
\hfill \mbox{\textit{Edexcel M3 2002 Q1 [6]}}