Calculating Maximum Speed and Acceleration

• What is the equation for maximum speed of an oscillator?


  v = ωA
• What does ω represent in the maximum speed equation?

  Angular frequency (rad s^-1)
• What does A represent in the maximum speed equation?

  Amplitude (m)
• At what position is the maximum speed of an oscillator achieved?

  At the equilibrium position (x = 0)
• What is the shape of the velocity-time graph when an oscillator starts at the equilibrium position?

  A cosine graph

  
• When is the speed of a mass on a spring zero?

  At its positive and negative amplitude
• If the maximum speed of an oscillator is 12 m s^-1 and the amplitude is 1.4 m, what is the frequency?

  1.4 Hz
• What is the equation for maximum acceleration of an oscillator?

  a = ωA
• When does maximum acceleration occur in an oscillator?

  When the gradient of the velocity-time graph is steepest

  
• At what position is the acceleration zero for an oscillator?

  At the equilibrium position (x = 0)
• How is angular frequency related to frequency?

  ω = 2πf
• How do you calculate frequency from maximum speed and amplitude?

  f = vmax / (2πA)
• What is the maximum acceleration of an oscillator with a time period of 0.4 s and amplitude of 2.8 m?

  690 m s^-2
• What is the formula for maximum acceleration in terms of time period and amplitude?

  amax = (2π/T)²A
• What are the key points about maximum speed and acceleration in oscillators?

  • Maximum speed occurs at equilibrium position.
  • Speed is zero at positive and negative amplitude.
  • Maximum acceleration occurs at maximum displacement.
  • Acceleration is zero at equilibrium position.
• What should you remember about notation in equations for oscillators?

  • Lowercase 'a' is for acceleration.
  • Uppercase 'A' is for amplitude.
  • Be confident moving between different equation forms.