12.1 Simple Harmonic Motion
Date, Section, Pages, etc.
Mr. Richter
Agenda
Warm Up
Any paper stragglers?
Intro to Simple Harmonic Motion
Notes:
Simple Harmonic Motion
Springs and Hooke’s Law
Simple Pendulums
Motion and Energy in SHM
Objectives: We Will Be Able To…
Identify the conditions of simple harmonic motion (SHM)
Explain how force, velocity, and acceleration change as an
object vibrates with simple harmonic motion.
Calculate the spring force using Hooke’s Law.
Warm Up
A metronome keeps a ticking count of 90 beats per minute.
1. What is its period of oscillation?
2. What is its frequency of oscillation?
Introduction to Simple Harmonic Motion
What keeps an object bouncing up and
down on a spring?
What would cause this to stop?
Simple Harmonic Motion (SHM)
Vibrations and Waves
Vibration: any repeated motion of an object moving back
and forth, or oscillating
Fans
Mass at the end of a spring.
Pendulums.
Waves are formed when a stationary substance vibrates.
Ripples in water.
Vibrating air with sound waves.
Whipping a rope.
Simple Harmonic Motion (SHM)
“any periodic motion that is the result of a restoring force
that is proportional to displacement”
Basically: back-and-forth motion over the same path.
Restoring Force: Object tends to want to return to original
position. (Location is “restored”).
Hooke’s Law (Springs!)
Most mass-spring systems obey a simple (proportional) relationship
between force and displacement.
This is also true of systems that can be modeled by a mass and spring.
This relationship is called Hooke’s Law
k = spring constant [N/m]
Force (F) always in opposite direction of displacement (restoring!)
The Simple Pendulum
Mass is called “bob”. Assume string is
weightless.
Restoring force is a component of the weight of
the bob.
Fg = mgsinθ
For small angles, the pendulum’s motion is simple
harmonic.
Energy During SHM
Total mechanical energy stays
the same.
Trade off between potential
and kinetic energy.
Motion during Simple Harmonic Motion
Wrap-Up: Did we meet our objectives?
Identify the conditions of simple harmonic motion (SHM)
Explain how force, velocity, and acceleration change as an
object vibrates with simple harmonic motion.
Calculate the spring force using Hooke’s Law.
Homework
p. 441 #e,4
p. 445 #1, 2, 4
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