4C.4.2 Simple harmonic motion Quiz: Pearson Edexcel Further Maths, Unit 33

The 20 questions

1. In simple harmonic motion, what is the acceleration of the particle?

   • constant in magnitude
   • proportional to displacement and directed away from equilibrium
   • proportional to the square of displacement
   • proportional to displacement and directed towards the equilibrium position

2. What is the period T of simple harmonic motion with angular frequency omega?

   • omega / (2 pi)
   • pi / omega
   • 2 omega / pi
   • 2 pi / omega

3. For SHM with amplitude a, which relation gives the speed v at displacement x?

   • v^2 = omega^2 (a^2 - x^2)
   • v = omega (a - x)
   • v^2 = omega^2 (a^2 + x^2)
   • v^2 = omega (a^2 - x^2)

4. The solution x = a cos(omega t) describes a particle that is at what position at t = 0?

   • at equilibrium, moving at speed a omega
   • at x = -a, moving
   • at x = 0, at rest
   • at x = a, at rest

5. What is the amplitude of simple harmonic motion?

   • the total distance covered in one period
   • the maximum displacement from the equilibrium position
   • the period of one oscillation
   • the speed at the equilibrium position

6. At the equilibrium position of SHM, the particle's

   • restoring force is maximum
   • speed is zero
   • acceleration is zero
   • displacement is maximum

7. In simple harmonic motion, where is the speed greatest?

   • at the extremities of the motion
   • where the acceleration is greatest in magnitude
   • at the centre of motion (equilibrium position)
   • at x = a only

8. A particle of mass m oscillates on a light elastic string of natural length l and modulus lambda with small oscillations. What is its period?

   • 2 pi sqrt(m/(lambda l))
   • pi sqrt(ml/lambda)
   • 2 pi sqrt(ml/lambda)
   • 2 pi sqrt(lambda/(ml))

9. A particle moves with x = 3 cos(2t). What is its period?

   • pi/2 s
   • 3 pi s
   • 2 pi s
   • pi s

10. SHM has angular frequency 4 rad/s and amplitude 2 m. What is the speed when x = 1 m?

    • 8 m/s
    • 12 m/s
    • 2 sqrt(3) m/s
    • 4 sqrt(3) m/s

11. SHM has angular frequency 3 rad/s and amplitude 0.5 m. What is the maximum acceleration?

    • 4.5 m/s^2
    • 1.5 m/s^2
    • 3 m/s^2
    • 9 m/s^2

12. A particle in SHM has period 2 s. What is its angular frequency?

    • pi/2 rad/s
    • pi rad/s
    • 2 rad/s
    • 4 pi rad/s

13. SHM has angular frequency 5 rad/s and amplitude 0.4 m. What is the maximum speed?

    • 2 m/s
    • 12.5 m/s
    • 5 m/s
    • 0.08 m/s

14. A particle in SHM with omega = 2 rad/s has speed 6 m/s at the centre. What is its amplitude?

    • 12 m
    • 6 m
    • 3 m
    • 1.5 m

15. A particle of mass 0.5 kg hangs on a light elastic string of natural length 0.8 m with modulus 8 N. What is the angular frequency of small oscillations?

    • 4 rad/s
    • 2 sqrt(5) rad/s
    • 20 rad/s
    • sqrt(5) rad/s

16. A particle has acceleration a = -9(x - 2). What is its period of oscillation?

    • 6 pi
    • 2 pi/3
    • pi/3
    • 2 pi/9

17. A particle in SHM has speed 4 m/s at displacement 3 m and speed 3 m/s at displacement 4 m, both on the same side of the centre. What is the amplitude?

    • sqrt(7) m
    • 5 m
    • 4 m
    • 7 m

18. In SHM of amplitude a, at what displacement are the kinetic and potential energies equal?

    • a/2
    • a/3
    • a/sqrt(2)
    • a sqrt(2)

19. Why is the period of SHM independent of its amplitude?

    • Because the acceleration is -omega^2 x, so omega depends only on the restoring constant, not the amplitude
    • Because the speed is constant throughout
    • Because amplitude cancels in the energy equation
    • Because gravity acts uniformly on the particle

20. A particle has x = 5 cos(pi t/2). At what first time is x zero?

    • pi s
    • 1 s
    • 2 s
    • 0.5 s

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