| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Year | 2013 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Small oscillations: rigid body compound pendulum |
| Difficulty | Challenging +1.2 This is a standard compound pendulum problem requiring parallel axis theorem application and SHM period derivation. Part (a) is routine bookwork showing radius of gyration using I = mk². Part (b) requires writing τ = Iα for small angles and identifying ω², which is methodical but involves multiple standard steps with Further Maths mechanics content, placing it moderately above average difficulty. |
| Spec | 6.04b Find centre of mass: using symmetry6.05f Vertical circle: motion including free fall |
A uniform square lamina S has side 2a. The radius of gyration of S about an axis through a vertex, perpendicular to S, is k.
**(a)** Show that $k^2 = \frac{8a^2}{3}$.
(4 marks)
**(b)** By writing down an equation of rotational motion for S, find the period of small oscillations of S about its position of stable equilibrium.
The lamina S is free to rotate in a vertical plane about a fixed smooth horizontal axis which is perpendicular to S and passes through a vertex.
(5 marks)
---2. A uniform square lamina $S$ has side $2 a$. The radius of gyration of $S$ about an axis through a vertex, perpendicular to $S$, is $k$.
\begin{enumerate}[label=(\alph*)]
\item Show that $k ^ { 2 } = \frac { 8 a ^ { 2 } } { 3 }$.
The lamina $S$ is free to rotate in a vertical plane about a fixed smooth horizontal axis which is perpendicular to $S$ and passes through a vertex.
\item By writing down an equation of rotational motion for $S$, find the period of small oscillations of $S$ about its position of stable equilibrium.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M5 2013 Q2 [9]}}