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# Intro to Simple Harmonic Motion (Horizontal Springs)

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Sections
Spring Force (Hooke's Law)
Intro to Simple Harmonic Motion (Horizontal Springs)
Energy in Simple Harmonic Motion
Simple Harmonic Motion of Vertical Springs
Simple Harmonic Motion of Pendulums
Energy in Pendulums

Concept #1: Intro to Simple Harmonic Motion

Example #1: Example

Practice: A mass-spring system with an angular frequency ω = 8π rad/s oscillates back and forth. (a) Assuming it starts from rest, how much time passes before the mass has a speed of 0 again? (b) How many full cycles does the system complete in 60s?

Concept #2: Equations of Simple Harmonic Motion

Practice: A 4-kg mass on a spring is released 5 m away from equilibrium position and takes 1.5 s to reach its equilibrium position. (a) Find the spring’s force constant. (b) Find the object’s max speed.

Example #2: Example

Practice: What is the equation for the position of a mass moving on the end of a spring which is stretched 8.8cm from equilibrium and then released from rest, and whose period is 0.66s? What will be the object’s position after 1.4s?

Example #3: Example