A2 Physics Oscillations

A2 Physics Oscillations

1. Free and forced oscillations

   • Oscillations
     • An object oscillates when it moves back and forth repeatedly, on either side of some equilibrium position
       • Used in pleasure, music and timing
   • Free oscillations
     • Objects that vibrate at their natural frequency
       • Natural frequency
         • The particular frequency in which an object oscillates
   • Forced oscillations
     • When an object causes an oscillating object to vibrate at a frequency that is not their natural frequency
       • Vibrates at the forcing frequency of the driving force

2. Observing oscillations

   • Anything faster than 5 Hz we cannot observe (it becomes a blur)
     • We use models to observe that oscillate at a lower frequency

3. Describing oscillations

   • An oscillating object accelerates towards the center of the oscillation and is moving fastest at the center.
     • It decelerates as it moves towards the end of the oscillation and at the extreme position, it stops for a moment and reverses the direction to repeat the cycle
   • Amplitude, period and frequency
     • Can plot the displacement-time graph of an oscillating object
       • The shape of graph is a sine/cosine curve and is described as sinusoidal
     • Displacement changes between positive and negative values
     • Amplitude
       • Maximum dispalcement
       • Symbol is x(o)
     • Can be used to show period and time
       • Period is the time it takes for one oscillation
       • Each are related as the inverse of each other
       • Frequency is the number of oscillations per second
   • Phase
     • The point that an oscillating mass has reached within the complete cycle of an oscillation
     • Phase difference
       • The amount by which two points are out of step with each other
         • Measured as a fraction, degrees or radians

4. Simple harmonic motion

   • When a pure sound wave travels through air, the molecules of the air vibrate in shm
   • When an alternating current flows in a wire, the electrons move in shm
   • When there is a small alternating current in a radio or TV arsenal when it is tuned to a signal, the electrons move in shm
   • The atoms that make up a molecule vibrate with shm e.g. hydrogen molecule
   • The requirements for shm
     • A mass that oscillates
     • A position where the mass is in equilibrium
     • A restoring force that acts to return the mass to its equilibrium position
       • The restoring force F is directly proportional to the displacement x of the mass from its equilibrium position and is directed towards that point
   • The changes of velocity is shm
     • As an object oscillates back and forth, its velocity constantly changes as it is constantly accelerating
       • It has a positive velocity when displacement is positive and negative velocity when displacement is negative
         • There are no sudden changes in velocity

5. Representing shm graphically

   • Displacement-time graph
   • Velocity-time graph
   • Acceleration-time graph

6. Frequency and angular frequency

   • Complete oscillation can be written as 2pi radians (360 degrees)
   • The phase of the oscillation changes by 2pi rad during one oscillation
   • If there are f oscillations in unit time (per second), there must be 2pi x f radians per unit time
     • This is known as angular frequency
       • Calculated as 2 x pi x frequency or 2 x pi / Period
       • Symbol as omega (lowercase)
       • Is the same as angular velocity (Displacement per unit time)

7. Equation of shm

   • Acceleration and displacement
     • The greater that an object travels from its equilibrium position, the larger the restoring force
       • Assuming mass is constant, the acceleration will increase if force increases
         • Displacement and acceleration act in opposite directions
           • A body executes simple harmonic motion if its acceleration is directly proportional to its displacement from its equilibrium position, and in opposite direction to its displacement
   • What type of graph to think in
     • Displacement time graph is a sine curve if the time starts at the equilibrium position
       • Displacement time graph is a cosine curve if the time starts at the amplitude
         • Velocity equation is created by differentiating the displacement equation (with time as a function)
           • Acceleration equation is created by differentiating the velocity equation ( with time as a function)

8. Energy changes in shm

   • Constant interchange of energy between two forms
     • Kinetic energy
     • Potential energy
   • At amplitude, potential energy is at its maximum and there is no kinetic energy
     • At equilibrium, kinetic energy is at its maximum and there is no potential energy
       • At positive displacement, potential energy changes to kinetic energy
       • At negative displacement (same direction), kinetic energy changes to potential energy
   • Energy graphs

9. Damped oscillations

   • In principle, oscillations go on forever, but in reality there is always friction that causes oscillations to die out
     • Amplitude decreases over time
       • The amplitude of an object's oscillation decreases as the function transfers energy away from her to the surroundings
   • The amplitude doesn't decrease linearly. It decays exponentially with time
     • At first the object oscillates rapidly, so there is large air resistance and loses energy quickly
       • As the object oscillates slowly, there are less amounts of air resistance, so energy is lost at a slower rate
   • Energy and damping
     • Damping is used if we want to get rid of vibrations
       • Used in suspension to make sure the car doesn't vibrate as the wheels move
       • Used in buildings to reduce the amount they vibrate during an earthquake
       • Without damping, energy is conserved in the mechanical system

10. Resonance

    • When an object oscillates with its maximum amplitude because the driving frequency matches the objects natural frequency
      • Its natural frequency is equal to the frequency of the driver
      • Its amplitude is maximum
      • It absorbs the greatest possible energy from the driver
    • Critical damping means the minimum amount of damping required to prevent an oscillation
      • Used in door hinges and car suspension
    • Used in MRI
      • Certain nucleus absorbs certain frequencies from the radio waves transmitted
    • Problems with things such as earthquakes
    • Used in microwaves
      • Microwaves matches the natural frequency of the water molecules and cause them to vibrate and heat up

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