In SHM the acceleration is proportional to displacement and opposite in direction, written a = −ω²x, so this Year 13 sheet opens with the defining quadratic acceleration. The angular frequency relation ω = 2π ÷ T and the answer x = A cos(ωt) appear in the key.
Key Takeaways
In SHM acceleration is proportional to displacement and opposite in direction (Q1).
SHM acceleration is a = −ω²x (Q2).
Q3 records ω = 2π ÷ T.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.In SHM, the acceleration is
(a) proportional to the displacement and in the opposite direction(b) proportional to the velocity(c) proportional to time(d) proportional to the square of the displacement
2.The equation for the acceleration in SHM is
(a) a = −ω²x(b) a = ω²x(c) a = ωx(d) a = −ωx
3.The angular frequency ω is related to the period by
(a) ω = 2π ÷ T(b) ω = T ÷ 2π(c) ω = 2πT(d) ω = 1 ÷ T
4.At the equilibrium position in SHM, the velocity is
(a) maximum(b) zero(c) equal to ω(d) negative
5.At maximum displacement in SHM, the acceleration is
(a) maximum(b) zero(c) constant(d) minimum
6.The displacement in SHM can be written as
(a) x = A cos(ωt)(b) x = Aωt(c) x = At²(d) x = A sin(ωt) only when A = 0
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Write the defining equation of SHM.
8.Write the relationship between ω and T.
9.What is the amplitude of SHM?
10.What is the phase difference between the displacement and the velocity in SHM?
11.Where is the kinetic energy maximum in SHM?
12.Where is the potential energy maximum in SHM?
13.Write the formula for the maximum speed in SHM.
14.What is the frequency of SHM with a period of 0.5 s?
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A pendulum has a period of 2 s. Using ω = 2π ÷ T, find the angular frequency.
16.A mass oscillates with ω = 4 rad/s. Using T = 2π ÷ ω, find the period.
17.An oscillation has an amplitude of 0.2 m and ω = 5 rad/s. Using v_max = Aω, find the maximum speed.
18.A mass on a spring has a period of 0.5 s. Using f = 1 ÷ T, find the frequency.
19.An oscillation has an amplitude of 0.1 m and ω = 10 rad/s. Using a_max = Aω², find the maximum acceleration.
20.A mass oscillates with a frequency of 2 Hz. Using ω = 2πf, find the angular frequency.
Answer Key
1. a) proportional to the displacement and in the opposite direction
2. a) a = −ω²x
3. a) ω = 2π ÷ T
4. a) maximum
5. a) maximum
6. a) x = A cos(ωt)
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
In SHM, how does acceleration relate to displacement?
Proportional and opposite in direction, option (a) in this worksheet (Q1).
What is the SHM acceleration equation?
a = −ω²x, option (a) in this worksheet (Q2).
What is ω in terms of the period?
ω = 2π ÷ T, option (a) in this worksheet (Q3).
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