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CAIE A-Level Physics A2 17.2 Energy in Simple Harmonic Motion Questions

Practise analysing kinetic, potential and total energy through SHM, explaining energy interchange and calculating energy at different positions.

Syllabus
2028–2030
Course
Physics 9702
Level
A2

Exam points

  • explain kinetic–potential energy interchange in SHM
  • calculate total SHM energy using E = 1/2mω²x₀² and relate it to energy at different positions

Covered syllabus points

17.2.1—The interchange between kinetic and potential energy during simple harmonic17.2.2—E = 1/2 mω2x0 2 for the total energy of a system undergoing simple harmonic

Question 1

[Maximum number: 3]

A small steel sphere is oscillating vertically on the end of a spring, as shown in Fig. 4.1.

Fig. 4.1

Fig. 4.1

The velocity v of the sphere varies with displacement x from its equilibrium position according to

v=±9.7(11.6−x2)v= \pm 9.7 \sqrt{\left(11.6-x^{2}\right)}

where v is in cms−1\mathrm{cms}^{-1} and x is in cm .

Describe, without calculation, the interchange between the potential energy and the kinetic energy of the oscillations.

Question 2

[Maximum number: 2]

A block of mass m oscillates vertically on a spring, as shown in Fig. 4.1.

Fig. 4.1

Fig. 4.1

The acceleration a of the block varies with displacement x from its equilibrium position, as shown in Fig. 4.2.

Fig. 4.2

Fig. 4.2

The amplitude of the oscillations is 3 Y and the maximum acceleration is 2 A.

Deduce expressions, in terms of some or all of m, A and Y, for:

the energy E of the oscillations.

E=
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