Chapter 11 Damping and Resonance © 2014 Pearson Education, Inc.

Damped Harmonic Motion If friction and drag are not negligible, you get “damped harmonic motion”. KE and PE transform into thermal energy which reduces the time and amplitude of oscillations. © 2014 Pearson Education, Inc.

Underdamping: most real life situations show a few small oscillations before the oscillator comes to rest (Top picture and Graph A) Critical damping: this is the fastest way to get to equilibrium with no oscillations (Graph B) Overdamping: the motion of the system is slowed so much that it takes a long time to get to equilibrium, but there is no oscillation at all (Graph C) Types of Damped Harmonic Motion © 2014 Pearson Education, Inc. SEVERLY underdamped

Systems where damping is unwanted: clocks, watches Systems where critical damping is wanted: car shock absorbers, earthquake shock absorbers, door closing mechanism Try to prevent this natural phenomena to get SHM Try to get this critical dampening As these shock absorbers wear out – you get underdamping, so car bounces, door slams

When an oscillating system is set into motion, it oscillates at its natural frequency/period. Examples: each guitar string has its own natural frequency, period of spring/pendulum If an external force is applied that has its own frequency, you get forced oscillations. Natural frequency and Forced Oscillations © 2014 Pearson Education, Inc. p

If the frequency of the external force is the same as the natural frequency, the amplitude becomes quite large. This is called resonance. Resonance is useful in paddleball, microwaves, music, tv/radio receivers Paddle ball and resonance: Success comes when you hit the ball again and again and again at only one specific frequency, only one rhythm that prevents you from flailing wildly at the stupid little red ball. This is the paddle’s resonant frequency. Resonance © 2014 Pearson Education, Inc.

Like damping, resonance can be wanted or unwanted. Shake objects at their resonant frequency and the back-and-forth motion can spell trouble. Each push adds more and more energy to the object—energy that, if not dissipated, starts to wreak havoc. Chinook Ground Resonance Test (33sec) The rotating blades begin to shake the airframe at its resonant frequency, and physics takes care of the rest: Because the blades are unable to dissipate the excess energy, the convulsions rend them from the fuselage. Glass breaking (42sec) Narrows Bridge (4.3min) General resonance, music, boats and earthquakes (Seattle built on soft sediments) (5.5min)

The sharpness of the resonant peak depends on the damping. No damping – huge amplitude change Shock absorbers on cars and buildings try to have heavy damping to prevent resonance f 0 =natural frequency