Foundations of Physics CPO Science Foundations of Physics Unit 5, Chapter 19

Why do some objects move back and forth around an equilibrium position while others don’t? Your answer Reasoning

Chapter 19 Harmonic Motion Unit 5: Waves and Sound Chapter 19 Harmonic Motion 19.1 Harmonic Motion 19.2 Why Things Oscillate 19.3 Resonance and Energy

Chapter 19 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 19 Vocabulary Terms harmonic motion cycle period frequency amplitude hertz (Hz) damping periodic force Resonance oscillator phase phase difference equilibrium restoring force natural frequency steady state

19.1 Harmonic motion Key Question: How do we describe the back and forth motion of a pendulum? *Students read Section 13.1 AFTER Investigation 13.1

What is Harmonic Motion? communications sound clocks nature

Harmonic motion is any motion that repeats

Oscillation “I oscillated between wearing a green shirt and a blue shirt.” Oscillate: to go back and forth Oscillation: a motion that repeats regularly Oscillator: something that goes back and forth; starts at a position and returns to it over and over. A pendulum is an oscillator. Vibration: a fast oscillation

Cycles, systems, and oscillators A cycle is the unit of motion that repeats as an oscillator moves. What are some other CYCLES you can think of?

Period v Frequency Seconds/cycle Cycles/second Period: the time it takes to complete one cycle; measured in SECONDS Seconds/cycle Frequency: how many cycles can occur in one second; measured in HERTZ Cycles/second

Period v Frequency Period refers to the time it takes something to happen. Frequency refers to how often something happens. Frequency is a rate quantity. Period is a time quantity.

Amplitude describes the size of a cycle. how far from equilibrium the object moves.

How does energy relate to amplitude?

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.

19.1 Summary: Harmonic motion is different from linear motion because it repeats. An oscillator is something that repeats a motion called an oscillation. The motion that repeats is called the cycle. The time it takes for one cycle is the period; the number of cycles that can occur in a second is the frequency, which is measured in hertz.

What do you know? Draw an original representation of harmonic motion. Explain how the terms you learned relate directly to your drawing Create a concept map of the terms you learned (a representation of how they are related)

19.2 Linear Motion vs. Harmonic Motion Graphs

19.2 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.

19.2 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.

Video clip 2:50 – 3:10

19.3 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.

19.3 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 net force.

19.3 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). Systems in harmonic motion must have a restoring force

19.3 The natural frequency The natural frequency is the frequency at which a system tends to oscillate when disturbed. Everything that can oscillate has a natural frequency and most systems have more than one. It doesn’t matter how many times you set your pendulum in motion, or at what angle, it will have the same natural frequency (and therefore period) Adding a steel nut greatly increases the inertia of a stretched rubber band, so the natural frequency decreases.

Can the natural frequency (or period) change? Natural frequency depends on a balance between restoring force and inertia Changing the mass changes the natural frequency ONLY if the restoring force is not due to gravity! This is because , just like free fall, the added inertia is equal to the added force from gravity. Gravity is independent of mass!

How do you change the natural frequency (or period) of a pendulum? The natural frequency depends only on the length of the string. Longer string means the restoring force is spread over a greater distance = longer period The strings on a guitar are changed by varying the tension on the string

19.3 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.

19.3 Resonance and Energy Resonance occurs when the periodic force has the same frequency as the natural frequency as the system. Energy is added at the right time, greater amplitude results. When resonance occurs, the amplitude response is very large compared to the strength of the force applied

19.3 Resonance A good way to understand resonance is to think about three distinct parts of any interaction between a system and a force.

Examples of resonance Shattering wine glass Force applied at the natural frequency, the amplitude builds up until it shatters Swinging on swing set you learn to “pump”, or push someone, at the natural frequency of the swing amplitude of swing builds up = larger swing Tacoma Narrows Bridge Read page 428-429 (hmmm, very interesting!)