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CAIE A-Level Physics 17.2 Energy in Simple Harmonic Motion

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

17.2 Energy in simple harmonic motion question 1

[Maximum number: 1]

A spring is hung vertically from a fixed point. A mass M is hung from the other end of the spring, as illustrated in Fig. 3.1.

Fig. 3.1

Fig. 3.1

The mass is displaced downwards and then released. The subsequent motion of the mass is simple harmonic.

The variation with time t of the length L of the spring is shown in Fig. 3.2.

Fig. 3.2

Fig. 3.2

State:

one time at which the spring has maximum elastic potential energy.
time = s

17.2 Energy in simple harmonic motion question 2

[Maximum number: 3]

A small wooden block (cuboid) of mass m floats in water, as shown in Fig. 3.1.

Fig. 3.1

Fig. 3.1

The top face of the block is horizontal and has area A. The density of the water is ρ\rho.

The block is now placed in a liquid with a greater density. The block is displaced and released so that it oscillates vertically. The variation with displacement x of the acceleration a of the block is measured for the first half oscillation, as shown in Fig. 3.3.

Fig. 3.3

Fig. 3.3

The mass of the block is 0.57 kg .

Use Fig. 3.3 to determine the decrease ΔE\Delta E in energy of the oscillation for the first half oscillation.
E= J

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