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CAIE A-Level Physics 17.1.4 SHM Velocity Equations

Practise using v = v₀ cos ωt or v = ±ω√(x₀²−x²) to calculate SHM velocity, then interpreting sign, amplitude, displacement and maximum speed.

Syllabus
2028–2030
Course
Physics 9702
Level
A2

Exam points

  • calculate velocity in SHM using v = v₀ cos ωt or v = ±ω√(x₀²−x²)
  • rearrange the velocity relationship to determine amplitude, displacement or angular frequency
  • interpret the sign and maximum velocity at different positions in the oscillation

17.1.4—The equations v = v0 cos ωt and v = ± ω ()xx0 22− 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 maximum speed
maximum speed = ms−1\mathrm{ms}^{-1}

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