AQA A Level Physics

Revision Notes

6.2.3 Calculating Maximum Speed & Acceleration

Maximum Speed

  • The speed v of an oscillator will vary in SHM. It is:
    • Maximum at the equilibrium position (x = 0)
    • Zero at the amplitude (x = A)

 

  • The maximum speed, vmax, is given by the equation:

vmax = ωA

  • Where:
    • vmax  = maximum velocity (m s-1)
    • ω = angular frequency (rad s-1)
    • A = amplitude (m)

Speed SHM graph, downloadable AS & A Level Physics revision notes

The variation of the speed of a mass on a spring in SHM over one complete cycle

Worked Example

Calculate the frequency of an oscillator with a maximum velocity of 12 m s-1 and amplitude of 1.4 m.

Step 1: State the known values

    • Maximum velocity, vmax = 12 m s-1
    • Amplitude, A = 1.4 m

Step 2: Write down the equation 

vmax = ωA

Step 3: Rewrite angular velocity in terms of frequency f

ω = 2πf

vmax = 2πfA

Step 4: Rearrange for frequency, f 

Max Velocity Worked Example Equation 1

Step 5: Substitute in the values

Max Velocity Worked Example Equation 2

Maximum Acceleration

  • The acceleration a of an oscillator will also vary in SHM. It is:
    • Maximum at the amplitude (x = A)
    • Zero at the equilibrium position (x = 0)

 

  • This is because the acceleration is directly proportional to the displacement of an oscillator
  • The maximum acceleration is given by the equation:

amax = ω2A

  • Where:
    • amax = maximum acceleration (m s2)
    • ω = angular frequency (rad s-1)
    • A = amplitude (m)

 

  • Although at the amplitude, the speed is zero, the oscillator has changed direction
  • This means that it has a non–zero velocity, and since acceleration is the rate of change of velocity, the oscillator has an acceleration at the amplitude too

Worked Example

Calculate the maximum acceleration of an oscillator with a time period of 0.4 s and amplitude of 2.8 m.

Step 1: State the known values

    • Time period, T = 0.4 s
    • Amplitude, A = 2.8 m

Step 2: Write down the equation

amax = ω2A

Step 3: Rewrite maximum acceleration with time period T

Step 4: Substitute in the values

Exam Tip

Make sure not to get mixed up with lower case a (acceleration) and upper case A (amplitude)

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