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.
How do we describe the back and forth motion of a pendulum?
*Students read Section 13.1 AFTER Investigation 13.1
6.
13.1 Cycles, systems, and oscillators
A cycle is a unit of motion that repeats.
7.
13.1 Harmonic motion is common sound communications clocks nature
8.
9.
13.1 Amplitude
Amplitude describes the size of a cycle.
10.
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.
11.
13.1 Linear Motion vs. Harmonic Motion Graphs
12.
13.
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.
14.
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.
15.
13.2 Why Things Oscillate
Key Question:
What kinds of systems oscillate?
*Students read Section 13.2 AFTER Investigation 13.2
16.
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.
17.
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.
18.
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).
19.
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.
20.
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.
21.
13.3 Resonance and Energy
Key Question:
What is resonance and why is it important?
*Students read Section 13.3 AFTER Investigation 13.3
22.
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.
23.
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.
24.
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.