Chapter 13: Energy Flow and Power

 13.1 Harmonic Motion

 13.2 Why Things Oscillate

 13.3 Resonance and Energy

Chapter 13 Objectives   Identify characteristics of harmonic motion, such as cycles, frequency,

and amplitude.   Determine period, frequency, and amplitude from a graph of harmonic

motion.   Use the concept of phase to compare the motion of two oscillators.   Describe the characteristics of a system that lead to harmonic motion.   Describe the meaning of natural frequency.   Identify ways to change the natural frequency of a system.   Explain harmonic motion in terms of potential and kinetic energy.   Describe the meaning of periodic force.   Explain the concept of resonance and give examples of resonance.

Chapter 13 Vocabulary Terms   amplitude   damping   frequency   harmonic motion   hertz (Hz)   natural frequency   oscillator   period

  periodic force   periodic motion   phase   phase difference   piezoelectric effect   resonance   stable equilibrium   unstable equilibrium

Inv 13.1 Harmonic motion

Investigation Key Question:

How do we describe the back and forth motion of a pendulum?

13.1 Cycles, systems, and oscillators

A cycle is a unit of motion that repeats.

13.1 Harmonic motion is common sound

communications

clocks nature

13.1 Describing harmonic motion

 The period of an oscillator is the time to complete one cycle.

13.1 Describing harmonic motion  Frequency is closely

related to period.

 The frequency of an oscillator is the number of cycles it makes per second.

At a frequency of 100 Hz, an oscillating rubber band completes 100 cycles per sec.

13.1 Describing harmonic motion  The unit of one cycle per second is called a

hertz (Hz).

 When you tune into a station at 100.6 on the FM dial, you are setting the oscillator in your radio to a frequency of 100.6 megahertz (MHz).

13.1 Amplitude  Amplitude describes the size of a cycle.

 The value of the amplitude is the maximum amount the system moves away from equilibrium.

13.1 Amplitude  The energy of an oscillator is proportional to

the amplitude of the motion.

 Friction drains energy away from motion and slows the pendulum down.

 Damping is the term used to describe this loss.

13.1 Harmonic Motion Graphs  Graphs of linear motion do not show cycles.

13.1 Harmonic motion graphs

 Graphs of harmonic motion repeat every period, just as the motion repeats every cycle.

 Harmonic motion is sometimes called periodic motion.

13.1 Circles and the phase of harmonic motion

 Circular motion is very similar to harmonic motion.

 Rotation is a cycle, just like harmonic motion.

 One key difference is that cycles of circular motion always have a length of 360 degrees.

13.1 Circles and the phase of harmonic motion   The word “phase” means where the oscillator is in the

cycle.   The concept of phase is important when comparing one

oscillator with another.

Chapter 13: Energy Flow and Power

 13.1 Harmonic Motion

 13.2 Why Things Oscillate

 13.3 Resonance and Energy

Inv 13.2 Why Things Oscillate

Investigation Key Question: What kinds of systems

oscillate?

13.2 Why Things Oscillate  Systems that have harmonic

motion move back and forth around a central or equilibrium position.

 Equilibrium is maintained by restoring forces.

 A restoring force is any force that always acts to pull the system back toward equilibrium.

13.2 Inertia   Newton’s first law explains why harmonic motion

happens for moving objects.   According to the first law, an object in motion stays in

motion unless acted upon by a force.

13.2 Stable and unstable systems   Not all systems in equilibrium show harmonic motion

when disturbed.   In unstable systems there are forces that act to pull the

system away from equilibrium when disturbed.   Unstable systems do not usually result in harmonic

motion (don't have restoring forces).

13.2 The natural frequency  The natural frequency is

the frequency at which systems tend to oscillate when disturbed.

 Everything that can oscillate has a natural frequency, and most systems have more than one.

Adding a steel nut greatly increases the inertia of a stretched rubber band, so the natural frequency decreases.

13.2 Changing the natural frequency   The natural frequency is proportional to the acceleration

of a system.   Newton’s second law can be applied to see the

relationship between acceleration and natural frequency.

Chapter 13: Energy Flow and Power

 13.1 Harmonic Motion

 13.2 Why Things Oscillate

 13.3 Resonance and Energy

Inv 13.3 Resonance and Energy Investigation Key Question: What is resonance and why is it important?

13.3 Resonance and Energy   Harmonic motion involves both potential energy and

kinetic energy.   Oscillators like a pendulum, or a mass on a spring,

continually exchange energy back and forth between potential and kinetic.

13.3 Resonance  A good way to understand resonance is to think

about three distinct parts of any interaction between a system and a force.

13.2 Resonance

 Resonance occurs when the frequency of a periodic force matches the natural frequency of a system in harmonic motion.

13.3 Energy, resonance and damping  Steady state is a balance between damping from

friction and the strength of the applied force.

 Dribbling a basketball on a floor is a good example of resonance with steady state balance between energy loss from damping and energy input from your hand.

  The precise heartbeat of nearly all modern electronics is a tiny quartz crystal oscillating at its natural frequency.

  In 1880, Pierre Curie and his brother Jacques discovered that crystals could be made to oscillate by applying electricity to them.

  This is known as the piezoelectric effect.

Quartz Crystals