C.1- Simple Harmonic Motion

• What is the symbol for angular frequency?


  ω
• What is the formula for angular frequency in terms of period?


  ω = 2π/T
• What is the formula for angular frequency in terms of frequency?

  ω = 2πf
• What does it mean for a motion to be isochronous?


  It means the time period remains constant.
• What is the base equation for acceleration in simple harmonic motion (SHM)?


  a = -ω²x
• How is simple harmonic motion (SHM) defined?


  SHM is an oscillation where acceleration is proportional and opposite to displacement.
• What is the maximum displacement in SHM called?

  Amplitude (X₀)
• What is the total mechanical energy in SHM represented by?


  Eₜ
• What is the relationship between kinetic energy (Eₖ) and potential energy (Eₚ) in SHM?


  Eₖ + Eₚ = Eₜ
• What does the equation x = x₀ \sin(ωt + φ) represent in SHM?

  It represents the displacement as a function of time, starting at the origin.
• What is the relationship between acceleration and displacement in SHM?


  a α -x
• What are the key characteristics of simple harmonic motion (SHM)?


  • Isochronous: time period remains constant
  • Acceleration is proportional and opposite to displacement
  • Examples include pendulums, mass-spring systems, and vibrating strings
• How does the time period of a simple pendulum change with length?


  A shorter length results in a smaller time period.
• What is the hypothesis for the mass-spring experiment?


  The spring constant will remain the same for all masses used.
• What is the relationship between T² and mass in the mass-spring system?


  T² ∝ m
• What does the graph of energy in SHM show over time?


  The total energy remains constant while kinetic and potential energy vary.
• How do the equations for displacement, velocity, and acceleration change with position in SHM?


  The equations can change based on the phase of the motion.
• What is the significance of the phase difference in SHM?

  It indicates the starting point of the oscillation.
• What is the relationship between the time period and mass in a mass-spring system?

  The time period increases with increasing mass.
• What is the effect of increasing the length of a pendulum on its time period?

  Increasing the length increases the time period.
• How does the energy in SHM relate to the displacement from equilibrium?


  Energy is maximum at maximum displacement and zero at equilibrium.
• What is the natural frequency of an oscillator?


  It is the frequency at which every oscillator vibrates after an initial disturbance.
• What is the forced or driving frequency?


  It is the frequency of an applied external force.
• What is free oscillation?


  Free oscillation occurs when a system oscillates without an external force being applied.
• What is forced or driving oscillation?

  Forced oscillation occurs when a system oscillates due to an external force.
• What is damping in oscillating systems?


  Damping is the loss of energy to surroundings, which decreases the amplitude of oscillation.
• What is resonance?


  Resonance is the increase in amplitude when the forced frequency is in phase with the natural frequency.
• What are the differences between free and forced oscillation?


  • Free oscillation: No external force applied, natural frequency.
  • Forced oscillation: External force applied, oscillates at forced frequency.
• What happens to an oscillating system due to damping?


  • Loses energy to surroundings.
  • Mainly caused by air resistance.
  • Amplitude decreases, but time period and frequency remain constant.
• What are the types of damping in oscillating systems?

  • Over-damped: No oscillation occurs.
  • Critically damped: Reduces amplitude in the shortest possible time.
  • Under-damped: Oscillations continue with gradually decreasing amplitudes.
• What is critically damped behavior in oscillating systems?


  Critically damped behavior reduces amplitude in the shortest possible time.
• What is over-damped behavior in oscillating systems?


  Over-damped behavior is when damping is so heavy that no oscillation occurs.
• What is under-damped behavior in oscillating systems?


  Under-damped behavior is when oscillations continue with gradually decreasing amplitudes.
• What are some examples of damping in real life?


  • Tuning radio
  • Grass bending
  • Pipe organ
  • Swinging
• What occurs during resonance in an oscillating system?


  Resonance occurs when the driving force frequency matches the natural frequency, increasing amplitude.
• What is the effect of heavy damping on amplitude?


  Heavier damping causes the amplitude to reduce faster.
• How does damping affect the time period and frequency of an oscillating system?


  Damping causes amplitude to decrease, but the time period and frequency remain constant.
• What is the relationship between natural frequency and forced frequency?

  • Natural frequency: Frequency of oscillation without external force.
  • Forced frequency: Frequency of oscillation due to an external force.