CIE A Level Physics (9702) 2019-2021

Revision Notes

19.1.5 SHM Graphs

SHM Graphs

  • The displacement, velocity and acceleration of an object in simple harmonic motion can be represented by graphs against time
  • All undamped SHM graphs are represented by periodic functions
    • This means they can all be described by sine and cosine curves
  • Key features of the displacement-time graph:
    • The amplitude of oscillations x0 can be found from the maximum value of x
    • The time period of oscillations T can be found from reading the time taken for one full cycle
    • The graph might not always start at 0
    • If the oscillations starts at the positive or negative amplitude, the displacement will be at its maximum
  • Key features of the velocity-time graph:
    • It is 90o out of phase with the displacement-time graph
    • Velocity is equal to the rate of change of displacement
    • So, the velocity of an oscillator at any time can be determined from the gradient of the displacement-time graph:

SHM Graphs equation 1

    • An oscillator moves the fastest at its equilibrium position
    • Therefore, the velocity is at its maximum when the displacement is zero
  • Key features of the acceleration-time graph:
    • The acceleration graph is a reflection of the displacement graph on the x axis
    • This means when a mass has positive displacement (to the right) the acceleration is in the opposite direction (to the left) and vice versa
    • It is 90o out of phase with the velocity-time graph
    • Acceleration is equal to the rate of change of velocity
    • So, the acceleration of an oscillator at any time can be determined from the gradient of the velocity-time graph:

SHM Graphs equation 2

    • The maximum value of the acceleration is when the oscillator is at its maximum displacement

Worked example: Using SHM graph data

Step 1:            The velocity is at its maximum when the displacement x = 0

Step 2:            Reading value of time when x = 0

From the graph this is equal to 0.2 s

Exam Tip

These graphs might not look identical to what is in your textbook, depending on where the object starts oscillating from at t = 0 (on either side of the equilibrium, or at the equilibrium). However, if there is no damping, they will all always be a general sine or cosine curves.

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