SHM Graphs

• What can be represented by graphs against time in SHM?

  Displacement, velocity, and acceleration

  
• What type of functions represent undamped SHM graphs?

  Periodic functions
• Which curves describe undamped SHM graphs?

  Sine and cosine curves
• How is velocity defined in relation to displacement?

  Velocity is the rate of change of displacement
• What is the formula for velocity in SHM?

  v = $\frac{s}{t}$
• How is acceleration defined in relation to velocity?

  Acceleration is the rate of change of velocity
• What is the formula for acceleration in SHM?

  a = $\frac{\Delta v}{t}$
• What are the characteristics of graphs starting from the equilibrium position in SHM?

  • Displacement-time graph: sine curve
  • Velocity-time graph: cosine graph, 90° out of phase
  • Acceleration-time graph: negative sine graph, 90° out of phase with velocity

  
• What are the characteristics of graphs starting from the amplitude position in SHM?

  • Displacement-time graph: cosine curve
  • Velocity-time graph: negative sine graph, 90° out of phase
  • Acceleration-time graph: negative cosine graph, 90° out of phase with velocity

  
• What are key features of displacement-time graphs in SHM?

  • Amplitude (A): maximum value of x
  • Time period (T): time for one full cycle
• How can velocity be determined from displacement-time graphs?

  • Velocity is the gradient of the displacement-time graph
  • Maximum velocity occurs at equilibrium position
• What is the relationship between acceleration and displacement in SHM?

  • Acceleration graph reflects displacement graph in x-axis
  • Positive displacement leads to negative acceleration

  
• How can acceleration be determined from velocity-time graphs?

  • Acceleration is the gradient of the velocity-time graph
  • Maximum acceleration occurs at maximum displacement
• When is the velocity of a swing at its maximum during SHM?

  When displacement x = 0
• At what time was the velocity of the swing first at its maximum?

  0.2 s
• What should you remember about SHM graphs in exams?

  • They may differ from textbook examples
  • They depend on the starting position of oscillation
  • No damping results in sine or cosine curves