Chapter 13: Energy Flow and Power 13.1 Harmonic Motion 13.2 Why Things Oscillate 13.3 Resonance and Energy 2

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. 3

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? 5

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 17

Inv 13.2 Why Things Oscillate Investigation Key Question: What kinds of systems oscillate? 18

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 25

Inv 13.3 Resonance and Energy Investigation Key Question: What is resonance and why is it important? 1. The restoring force pulls the pendulum toward the center (equilibrium). 2. The pendulum overshoots the center because of its inertia. 3. The restoring force pulls back toward the center, slowing and reversing the pendulum’s direction. 4. The pendulum overshoots the center again, because of inertia. 5. The cycle repeats, creating harmonic motion. 26

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.

Quartz Crystals 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.