# 12.1 Simple Harmonic Motion Date, Section, Pages, etc. Mr. Richter.

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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.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.  F g = mgsin θ  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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