Maximum Marks: 40Suggested time: 60 minutes
Instructions: Answer all 20 questions. Marks are shown in brackets. Show calculation steps and units. These are original practice questions, not an official examination paper.
Section A · 1-mark questions — 8 × 1 = 8 marks
- Define period.[1]
- Frequency-period relation?[1]
- Restoring force in SHM?[1]
- Where is speed maximum in SHM?[1]
- Where is acceleration magnitude maximum?[1]
- Spring angular frequency?[1]
- Small-angle pendulum period?[1]
- Total spring energy for amplitude A?[1]
Section B · 2-mark questions — 6 × 2 = 12 marks
- Period .5s: frequency?[2]
- m=.5kg,k=200N/m: period?[2]
- For x=Acosωt, acceleration?[2]
- Pendulum length becomes 4l: period factor?[2]
- Velocity at an extreme?[2]
- Condition for pendulum SHM approximation?[2]
Section C · 3-mark questions — 4 × 3 = 12 marks
- m=.5,k=200: angular frequency and period?[3]
- A=.1m,ω=4: maximum speed and acceleration?[3]
- Pendulum length 1m,g=9.8: period?[3]
- Describe energy in one SHM cycle.[3]
Section D · 4-mark questions — 2 × 4 = 8 marks
- k=50N/m,A=.2m: total energy and U at x=.1m?[4]
- Why does a real oscillator stop?[4]
End of paper — review signs, units and working.
Open marking scheme and model answers
Attempt the paper before opening the key. Model answers show the expected facts and results; mark allocation is a suggested guide and equivalent correct methods should receive credit.
Q1 · 1 mark
Time for one cycle.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q2 · 1 mark
f=1/T.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q3 · 1 mark
F=−kx.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q4 · 1 mark
At equilibrium.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q5 · 1 mark
At extreme displacement.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q6 · 1 mark
√(k/m).
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q7 · 1 mark
2π√(l/g).
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q8 · 1 mark
½kA².
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q9 · 2 marks
2 Hz.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.
Q10 · 2 marks
0.314 s.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.
Q11 · 2 marks
a=−ω²x.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.
Q12 · 2 marks
2.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.
Q13 · 2 marks
Zero.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.
Q14 · 2 marks
Small angular displacement.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.
Q15 · 3 marks
ω=20 rad/s; T≈0.314 s.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.
Q16 · 3 marks
0.4 m/s and 1.6 m/s².
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.
Q17 · 3 marks
≈2.01 s.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.
Q18 · 3 marks
K max/U min at equilibrium; U max/K zero at extremes; total energy constant without damping.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.
Q19 · 4 marks
E=1 J; U=.25 J.
Suggested split: 1 for principle, 1 for equation, 1 for working and 1 for result/explanation. Accept an equivalent correct method.
Q20 · 4 marks
Damping transfers mechanical energy into heat/sound and reduces amplitude.
Suggested split: 1 for principle, 1 for equation, 1 for working and 1 for result/explanation. Accept an equivalent correct method.