Oscillations

• Oscillations are repeated back-and-forth movements on either side of any equilibrium position
• Oscillator is a device that works on the principles of oscillations
• The shape of the displacement time graph of an oscillating system is a sine curve. this motion is called sinusoidal
• Displacement is the instantaneous distance of the oscillator from its equilibrium position
• Amplitude is the maximum displacement from the equilibrium position
• Period is the time taken for one complete oscillation
• Frequency is the number of complete oscillations per unit time
• Angular frequency is the rate of change of angular displacement
• One complete oscillation is the time taken for the oscillator to pass the equilibrium from one side and back again fully from the other side
• The period T = 1/f
• If an object has a natural frequency, it will vibrate with this frequency when disturbed slightly from its equilibrium position
• Phase difference is the measure of how much one wave is out of set with another wave
• In phase means when the relative position of two oscillators are equal
• Simple harmonic motion is the acceleration proportional to displacement directed towards a fixed point
• Requirements for simple harmonic motion

  • mass that oscillates
  • position where the mass is in equilibrium
  • restoring force that acts to return mass to equilibrium
• Maximum velocity at equilibrium position and minimum at extremes
• Free oscillation is the oscillatory motion that is not subjected to an external periodic driving force, oscillates at natural frequency
• Forced oscillation - oscillation caused by an external driving force, frequency is determined by the driving force
• Natural frequency is the unforced frequency of oscillation of a freely oscillating object
• During simple harmonic motion, energy is constantly exchanged between two forms, kinetic and potential
• The system has maximum kinetic energy when the displacement is zero because the object is at its equilibrium position and so moving at maximum velocity
• The total energy of a simple harmonic system always remains constant and is equal to the sum of the kinetic and potential energies
• The potential energy is at a maximum when the displacement is at a maximum
• Damped oscillations - reduction in amplitude of an oscillating system due to the dissipation of energy
• Damping is the reduction in energy and amplitude from an oscillating system due to the resistive forces acting on it
• Light Damping is when the system oscillates about equilibrium position with decreasing amplitude over a period of time
• Critical damping is when the system does not oscillate and returns to equilibrium position in the shortest possible time
• Heavy Damping is when the displaced object never oscillates but returns to its equilibrium position very slowly
• Driving frequency is the frequency of forced oscillations
• Resonance occurs when driving frequency matches natural frequency, resulting in maximum amplitude of oscillations
• Resonance occurs when the driving frequency applied to an oscillating system is equal to its natural frequency, the amplitude of the resulting oscillations increase
• Resonance happens because at resonance, energy is transferred from the driver to the oscillating system most efficiently. Resulting the system with the maximum kinetic energy possible
• Resonant Frequency is the frequency at which resonance occurs
• In a system in resonance,

  • its natural frequency is equal to the frequency of the driver
  • amplitude is maximum
  • absorbs the greatest possible energy from the driver
• Effects of damping on the frequency response of a system undergoing forced oscillations

  • decreases amplitude at all frequencies
  • slightly decrease the resonant frequency
  • resonant peak becomes flatter