The restoring force in SHM is proportional to displacement and the acceleration always points towards the equilibrium position, so this IB sheet opens with the two direction-fixing facts. Period is the time for one complete oscillation, with f = 1/T in the answers.
Key Takeaways
The restoring force in SHM is proportional to displacement (Q1).
Acceleration in SHM points towards equilibrium (Q2).
Q6 records f = 1/T.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.In simple harmonic motion, the restoring force is proportional to
(a) the displacement(b) the velocity(c) the acceleration of gravity(d) time
2.In SHM, the acceleration is always directed
(a) towards the equilibrium position(b) away from the equilibrium position(c) in the direction of motion(d) vertically upwards
3.At the equilibrium position in SHM, the velocity is
(a) maximum(b) zero(c) constant(d) negative
4.At maximum displacement (the amplitude), the velocity is
(a) zero(b) maximum(c) equal to the average speed(d) negative
5.The time period of SHM is the
(a) time for one complete oscillation(b) number of oscillations(c) maximum displacement(d) time for half an oscillation
6.The frequency f and period T of SHM are related by
(a) f = 1/T(b) f = T(c) f = 2T(d) f = T²
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Define simple harmonic motion.
8.State how the acceleration varies with the displacement in SHM.
9.What is the amplitude of SHM?
10.What is the time period of SHM?
11.Where is the velocity maximum in SHM?
12.What is the phase of an oscillation?
13.Write the formula linking frequency and period.
14.Give one example of a system that undergoes simple harmonic motion.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A pendulum completes 20 oscillations in 40 s. Using T = time ÷ number of oscillations, find the period.
16.A pendulum has a period of 2 s. Using f = 1/T, find the frequency.
17.A mass on a spring oscillates with a frequency of 5 Hz. Using T = 1/f, find the period.
18.A pendulum completes 30 oscillations in 60 s. Find the period.
19.A mass on a spring has a period of 0.5 s. Using f = 1/T, find the frequency.
20.A pendulum has a period of 4 s. Using f = 1/T, find the frequency.
Answer Key
1. a) the displacement
2. a) towards the equilibrium position
3. a) maximum
4. a) zero
5. a) time for one complete oscillation
6. a) f = 1/T
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the SHM restoring force proportional to?
The displacement, option (a) in this worksheet (Q1).
Where is SHM acceleration always directed?
Towards the equilibrium position, option (a) in this worksheet (Q2).
What is the period of oscillation?
The time for one complete oscillation, option (a) in this worksheet (Q5).
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