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CAIE A-Level Physics 17.1.3 Using a = −ω²x and x = x₀ sin ωt

Practise using a = -omega²x and x = x0 sin omega t in SHM, calculating acceleration or displacement, interpreting phase and checking signs, amplitudes and units.

Syllabus
2028–2030
Course
Physics 9702
Level
A2

Exam points

  • use a = −ω²x to calculate acceleration, displacement or angular frequency
  • use x = x₀ sin ωt to determine displacement or interpret phase and time
  • check signs, amplitude and angular-frequency units in an SHM equation

17.1.3—A = –ω2x and recall and use, as a solution to this equation, x = x0 sin ωt question 1

[Maximum number: 2]

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

Use data from Fig. 3.2 to determine, for the motion of the mass:

the magnitude of the maximum acceleration.
maximum acceleration = ms−2\mathrm{ms}^{-2}

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