oscillations

• What does displacement signify in oscillations?

  Distance from the oscillator to equilibrium
• What is the amplitude in simple harmonic motion?

  Maximum value of displacement
• How is the time period defined in oscillations?

  Time to complete one full oscillation
• What does frequency measure in oscillations?

  Number of oscillations per unit time
• What is angular frequency?

  Rate of change of angular displacement
• How is angular frequency denoted?

  By the symbol omega (ω)
• How does angular frequency differ from angular velocity?

  Angular frequency is a scalar quantity
• What is the defining characteristic of simple harmonic motion?

  Acceleration is proportional to displacement
• What direction is acceleration in simple harmonic motion?

  Towards the equilibrium position
• What is the defining equation of simple harmonic motion?

  a = -ω²x
• What does a straight line graph of acceleration versus displacement indicate?

  Acceleration is proportional to displacement
• What does the negative gradient in the acceleration-displacement graph signify?

  Acceleration is directed towards equilibrium
• How can we find important quantities from the acceleration-displacement graph?

  Using the gradient of the graph
• What does the gradient of the acceleration-displacement graph equal?

  -ω²
• How can we find the time period from the angular frequency?

  Using ω = 2π/T
• What is the relationship between frequency and time period?

  f = 1/T
• What is the setup needed to measure the frequency of a simple harmonic oscillator?

  A spring, lap stand, and fiducial marker
• How do we avoid parallax error in measurements?

  By measuring from eye level
• What is the importance of taking multiple measurements?

  To improve accuracy by finding the mean
• How do we calculate displacement using the equation x = a cos(ωt)?

  By substituting amplitude and time
• What must be ensured when using the equations for simple harmonic motion?

  Calculator must be in radian mode
• How do we find displacement two seconds after release for a spring with frequency 5 Hz?

  Use x = a cos(2πft)
• What is the displacement of a spring with amplitude 4 cm after 2 seconds?

  0.04 m
• What is the relationship between displacement and velocity in simple harmonic motion?

  Velocity is the rate of change of displacement
• How does the acceleration graph relate to the velocity graph?

  Acceleration is the rate of change of velocity
• What happens to the amplitude and time period with light damping?

  Amplitude decreases, time period remains the same
• How does heavier damping affect oscillations?

  Amplitude decreases more with each cycle
• What is the difference between free and forced oscillations?

  Free oscillations have no external forces
• What occurs during resonance in forced oscillations?

  Amplitude increases dramatically at natural frequency
• What happens to amplitude as frequency increases past natural frequency?

  Amplitude steadily decreases
• How does damping affect the resonance curve?

  Amplitude decreases and peak shifts left
• What is an example of resonance in a microwave oven?

  Driving frequency matches water molecules' frequency
• What is a problematic example of resonance?

  Oscillating bridge affected by wind
• What causes resonance in the examples provided?

  Driving frequency matches natural frequency
• What are the key characteristics of simple harmonic motion?

  • Acceleration is proportional to displacement
  • Acceleration directed towards equilibrium
  • Defined by the equation a = -ω²x
• What are the effects of damping on oscillations?

  • Amplitude decreases with each cycle
  • Time period remains the same
  • Heavier damping results in greater amplitude decrease
• What are the differences between free and forced oscillations?

  • Free oscillations: no external forces
  • Forced oscillations: external driving force present
  • Resonance occurs when driving frequency matches natural frequency
• What are the implications of resonance in practical examples?

  • Microwave ovens: increases kinetic energy of water molecules
  • Oscillating bridges: can lead to structural failure if not managed