Vibrations & Waves Part 1: Periodic Motion
Periodic motion: any motion that repeats in a regular cycle.
Mass on a Spring
Simple Harmonic Motion: When Force is directly proportional to Δx If we increase the mass, we increase the force, and increase the displacement
Hooke’s Law: the magnitude of the restoring force exerted by a spring is equal to the spring constant times the distance the spring is stretched or compressed from its equilibrium position.
Force is always in the opposite direction of the stretch or compression of the spring k, the spring constant, depends on the spring Δx is the distance the spring is stretched or compressed from its equilibrium position
Not all springs obey Hooke’s Law Rubber bands Those that do follow Hooke’s Law are called elastic springs Elastic springs can be stretched beyond their elastic limit where Hooke’s law no longer applies
Pendulums
Period (T): the time needed for an object to make one complete cycle.
Notice the period does NOT depend on the mass The period depends only on the length of the string and gravity
* The period of a pendulum also does not depend on amplitude. the maximum distance the object moves from equilibrium
Resonance occurs when forces are applied to a vibrating or oscillating object at time intervals equal to the period
Resonance in simple harmonic motion systems causes a larger and larger displacement as energy is added in small increments Resonance caused the Tacoma Narrows Bridge Collapse on November 7th, 1940