Physics 6B Lecture 1

# Physics 6B Lecture 1 - Physics 6B Lecture 1 Monday August 2...

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Physics 6B Lecture 1 18:03 Monday August 2, 2010 T: MTW 11-1225 Broida 1610 Professor: Jenna Hagemeler Office Hours: Tue and Wed 2-330pm Midterms: August 16, August 30 Final: September 9 730-1030 Homework: Due Thursday Sign in: PHYS6BHAGEMEIER Chapter 11: Elasticity and Periodic Motion *skipping Elasticity Goals for chapter 11 To follow periodic motion to a study of simple harmonic motion To solve equations of simple harmonic motion To use pendulum as a prototypical system undergoing simple harmonic motion To study how oscillations may be damped or driven

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Periodic Motion Any motion that repeats over and over o Oscillations about stable equilibrium position (spring) Simple harmonic motion: a special type of periodic motion, very important as an approximation to many systems o Mass on a spring o Simple pendulum (grandfather clock pendulums, swings) o Vibrating molecule o Light interacting with electrons o Electrons traveling through a crystal Simple harmonic motion with springs Mass on a spring = glider with spring on air track o Compressed spring x<0, F>0 o Equilibrium position x=0 o Stretched spring x>0, F<0 Force is a restoring force, pulling system back to equilibrium o Fx= -kx o Ax= Fx/m= -kx/m Terminology
Oscillation Restoring force SHM: force directly proportional to displacement Hooke’s Law Amplitude (A) in meters: maximum displacement Cycle: motion from Period (T) in seconds: time it takes for one cycle Frequency (f) in 1/s or Hz o F-1/T T=1/f 1Hz=1cycle/s=1s-1 Angular frequency ( ϖ ) in rad/s o ϖ =2pif=2pi/T Iclicker #1 Prediction for mass and spring! An object on the end of a spring is oscillating in a simple harmonic motion. If the object is now set to oscillate with an amplitude that is Twice as big, what happens to the frequency? (A) f increases by a factor of 2 (B) f decreases by a factor of 2 (C) f remains the same (D) f increases by a factor of sqrt(2) o A1, time= 15 sec, cycles= 10 T1= (15 sec/10)= 1.5 sec

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F1= (10/15 sec)= 2/3 Hz o A2= 2A1, T2= 1.6 sec F2= 10/16 Hz o Therefore, (C) f remains the same. Energy changes as the oscillator moves. Conserved in the absence of friction, energy converts between kinetic and potential Ax=amax o Vx=0 o –A o E is all potential energy Ax=.5amax o Vx=+ sqrt(3/4)vmax o -.5A o E is partly potential, partly kinetic energy Vx=+ vmax o 0A o E is all kinetic energy Ax=-.5amax o Vx=+ sqrt(3/4)vmax
o .5A o E is partly potential, partly kinetic energy Vx=-amax o Vx=0 o A o E is all potential energy E= (.5kA^2)= (.5mvx2+.5kx^2) Iclicker #2 To double the total energy of a mass-spring system oscillating in simple harmonic motion, the amplitude must increase by a factor of (A) 4. (B) 2sqrt(2)= 2.282. (C) 2. (D) sqrt (4)= 1.414.

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