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Oscillations

Velocity, period and graphical relationships

  • 2 things to know
  • Papers 1, 2 and 3

Overview

Recall questions on velocity and maximum velocity in simple harmonic motion with calculations, isochronous oscillators, gradients of displacement-time and velocity-time graphs, and the phase relationships between displacement, velocity and acceleration.

What you need to know

Answer each one before you reveal it.

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Key term

For simple harmonic motion, what do the gradients of the displacement-time and velocity-time graphs represent, and what happens to the period if the amplitude is increased?

Numbers

State the equation for maximum velocity in SHM.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Calculate the velocity magnitude when angular frequency = 15.5 rad s⁻¹, amplitude = 0.38 m, displacement = 0.32 m.

    Model answer

    Velocity magnitude = 15.5 × sqrt((0.38 × 0.38) - (0.32 × 0.32)) = 3.18 m s⁻¹.

  2. 2

    Calculate the maximum velocity when angular frequency = 15.5 rad s⁻¹, amplitude = 0.05 m.

    Model answer

    Maximum velocity = 15.5 × 0.05 = 0.775 m s⁻¹.

  3. 3

    What is the phase relationship between acceleration and displacement in SHM?

    Model answer

    They are in antiphase (π radians or 180° out of phase).

  4. 4

    On a velocity-time graph for simple harmonic motion, what physical quantity does the gradient at any point represent?

    Model answer

    The acceleration at that instant.

  5. 5

    State the equation for velocity in SHM in terms of displacement.

    Model answer

    v = ±ω√(A² − x²)

  6. 6

    At what position does maximum velocity occur in SHM?

    Model answer

    At the equilibrium position where x = 0.

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