| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics B AS (Further Mechanics B AS) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Prove SHM and find period: given force or equation of motion directly |
| Difficulty | Standard +0.8 This is a multi-part Further Mechanics question requiring derivation of spring stiffness from equilibrium, proving SHM from first principles using F=ma with variable spring extension, and finding period from the differential equation. While the individual steps follow standard SHM methodology, the question requires careful setup of forces, algebraic manipulation to show the specific form, and physical reasoning about model validity—more demanding than routine SHM problems but still within standard Further Maths scope. |
| Spec | 4.10f Simple harmonic motion: x'' = -omega^2 x4.10g Damped oscillations: model and interpret6.02d Mechanical energy: KE and PE concepts6.02h Elastic PE: 1/2 k x^2 |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (i) | E |
| Answer | Marks |
|---|---|
| h | C |
| Answer | Marks | Guidance |
|---|---|---|
| [1] | 3.4 | |
| 5 | (ii) | P |
| Answer | Marks |
|---|---|
| h h h | M1 |
| Answer | Marks |
|---|---|
| [4] | 3.4 |
| Answer | Marks |
|---|---|
| 1.1 | Using N2L with HL |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (iii) | h |
| Answer | Marks | Guidance |
|---|---|---|
| g | B1 | |
| [1] | 2.2a | oe |
| 5 | (iv) | No. Too large m would lead to spring being too |
| compressed. | E1 | |
| [1] | 3.5a | N |
Question 5:
5 | (i) | E
Using HL
mg
mg = kh so k (cid:32)
h | C
B1
[1] | 3.4
5 | (ii) | P
N2L ↓
S
mg
mg(cid:16) (cid:11)h(cid:14) y(cid:12)(cid:32)my
h
g g g
so g(cid:16) (cid:117)h(cid:16) (cid:117)y(cid:32) y and y(cid:14) y(cid:32)0 AG
h h h | M1
B1
A1
A1
[4] | 3.4
3.3
1.1
1.1 | Using N2L with HL
Use of h + y
All correct
Some working seen.
5 | (iii) | h
Period is 2(cid:83)
g | B1
[1] | 2.2a | oe
5 | (iv) | No. Too large m would lead to spring being too
compressed. | E1
[1] | 3.5a | N(i) Find an expression for the stiffness of the spring, $k \mathrm { Nm } ^ { - 1 }$, in terms of $m , h$ and $g$.
The particle is pushed down a further distance from the equilibrium position and released from rest. At time $t$ seconds, the displacement of the particle from the equilibrium position of the system is $y \mathrm {~m}$ in the downward direction, as shown in Fig. 5.3. You are given that $| y | \leq h$.\\
(ii) Show that the motion of the particle is modelled by the differential equation $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} t ^ { 2 } } + \frac { g y } { h } = 0$.\\
(iii) Find an expression for the period of the motion of the particle.\\
(iv) Would the model for the motion of the particle be valid for large values of $m$ ? Justify your answer.
\hfill \mbox{\textit{OCR MEI Further Mechanics B AS Q5 [7]}}