Chapter 11 Harmonic Motion Peter Anderson ander 324purdue

Chapter 11– Harmonic Motion Peter Anderson ander 324@purdue. edu Office: PHYS 221 Office Hours: Tuesday 12 pm to 2 pm

The prototypical oscillator involves a mass and a spring and is called the “simple harmonic oscillator”. k k where k m m m

Quiz 1 A particle undergoing simple harmonic oscillation of period T is at –A at time t=0. At time t = 2. 00 T is it at a) -A b) A c) 0 d) Between –A and 0 e) Between 0 and A

Quiz 2 A particle undergoing simple harmonic oscillation of period T is at –A at time t=0. At time t = 3. 50 T is it at a) -A b) A c) 0 d) Between –A and 0 e) Between 0 and A

Quiz 3 A particle undergoing simple harmonic oscillation of period T is at –A at time t=0. At time t = 5. 25 T is it at a) -A b) A c) 0 d) Between –A and 0 e) Between 0 and A

SHM and energy •

Quiz 4 •

Sample Problem 1 In the figure, a penguin (obviously skilled in aquatic sports) dives from a uniform board that is hinged at the left and attached to a spring at the right. The board has a length L = 2. 0 m and mass m = 12 k; the spring constant is k=1300 N/m. When the penguin dives, it leave the board and spring oscillating with a small amplitude. Assume that the board is stiff enough not to bend, and find the period T of the oscillations.

Damped Motion • With damped motion all three cases eventually lose all of their energy due to frictional forces • Under Damped – Still oscillates but eventually dies • Over Damped – Does not oscillate • Critically Damped – Approaches 0 energy in the fastest possible manner

Damped Motion

Quiz 5 If you were to design a bridge and found it had a resonance frequency. How would you want to damp this frequency? a) Over b) Under c) Critically

Quiz 6 Will this bowling ball hit me in the face? A. Yes B. No C. I hope so