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Physics 101:  Lecture 20  Elasticity and Oscillations ,[object Object],Exam III Tuned mass damper (pendulum) in Taipei 101
Review Energy in SHM ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],m x x=0 0 x PE S
Kinetic Energy ACT ,[object Object],[object Object]
Potential Energy ACT ,[object Object],[object Object],[object Object],[object Object],Look at time of maximum displacement  x =  A  Energy  = ½ k A 2  + 0   Same for both!
Kinetic Energy ACT PE =  1 / 2 kx 2   KE = 0 x=0 x=+A x=-A x=0 x=+A x=-A same for both PE = 0  KE = KE MAX same  for both ,[object Object],[object Object],[object Object]
Velocity ACT ,[object Object],[object Object],Same maximum Kinetic Energy K = ½ m v 2  smaller mass requires larger v
Review:  Simple Harmonic Motion Period = T  (seconds per cycle) Frequency = f = 1/T  (cycles per second) Angular frequency =    = 2  f = 2  /T 17
Simple Harmonic Motion: Quick Review x(t) =  [A]cos(  t) v(t) = -[A  ]sin(  t) a(t) = -[A  2 ]cos(  t) x(t) =  [A]sin(  t) v(t) = [A  ]cos(  t) a(t) = -[A  2 ]sin(  t) x max  = A v max  = A  a max  = A  2 Period = T  (seconds per cycle) Frequency = f = 1/T  (cycles per second) Angular frequency =    = 2  f = 2  /T OR 19
Period  T  of a Spring ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Demos:  A,m,k dependence
Period ACT ,[object Object],[object Object],+2A t -2A x CORRECT
Vertical Mass and Spring ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Vertical Spring ACT ,[object Object],[object Object],Y=0 Y=0 Just before being released, v=0 y=d E tot  = 0 + ½ k d 2   Same total energy for both When pass through equilibrium all of this energy will be kinetic energy again same for both! PE =  1 / 2 k y 2 PE =  1 / 2 k y 2
Pendulum Motion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],m L x T mg
Preflight 1 ,[object Object],[object Object],[object Object],CORRECT
Elevator ACT ,[object Object],[object Object],[object Object],[object Object]
ACT ,[object Object],[object Object],[object Object],[object Object],“ Effective g” is larger when accelerating upward (you feel heavier)
Elevator ACT ,[object Object],[object Object],[object Object],[object Object],“ Effective g” is larger when accelerating upward (you feel heavier) CORRECT
Alien Preflight  You're forgetting that I have an i-phone, so this would not require any physics knowledge. 4G babay! make a pendulum out of the shoelaces   Can you breathe? If not, you're on the moon.  .....what a creepy question... I will give my digital wristwatch to one of the space invaders and ask him where I am.  jump, duh If they've managed to create the technology to emulate Earth's gravity on their base where this room is located (and I don't see why they'd even do this) then this wouldn't work, but at that point you're way out of your league anyways. Supply and demand dictates that the watch will be worth more on the moon than on earth.  Supply and demand dictates that the watch will be worth more on the moon than on earth.
MacGyver I would then MacGyver my way out of the room using the shoelaces as a lockpick and the watch battery and wires from the watch as a makeshift taser to stun my captors, I'm not MacGyver.  Think like MacGyver and use the shoelaces and the wristwatch to make a explosvie device to blow out one of the walls. What you can do with this information only having a cheap digital wristwatch and a pair of shoes in a room with no windows, and you are not MacGyver, then you're pretty much screwed. If you are MacGyver, you'll be fine. Einstein's equivalence principal also states that you can be in a spacecraft accelerating at a strength equivalent to either the earth or the moon and you wouldn't know from this information whither or not you were on the earth, the moon, or a spaceship. why figure out where you are when you could use your sweet McGyver skills and use these objects to make a small explosive with which you can escape!
Preflight  ,[object Object],make a pendulum with the shoelace and shoes and use the wristwatch to determine the length of each period.
Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Lecture20

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  • 7. Review: Simple Harmonic Motion Period = T (seconds per cycle) Frequency = f = 1/T (cycles per second) Angular frequency =  = 2  f = 2  /T 17
  • 8. Simple Harmonic Motion: Quick Review x(t) = [A]cos(  t) v(t) = -[A  ]sin(  t) a(t) = -[A  2 ]cos(  t) x(t) = [A]sin(  t) v(t) = [A  ]cos(  t) a(t) = -[A  2 ]sin(  t) x max = A v max = A  a max = A  2 Period = T (seconds per cycle) Frequency = f = 1/T (cycles per second) Angular frequency =  = 2  f = 2  /T OR 19
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18. Alien Preflight You're forgetting that I have an i-phone, so this would not require any physics knowledge. 4G babay! make a pendulum out of the shoelaces Can you breathe? If not, you're on the moon. .....what a creepy question... I will give my digital wristwatch to one of the space invaders and ask him where I am. jump, duh If they've managed to create the technology to emulate Earth's gravity on their base where this room is located (and I don't see why they'd even do this) then this wouldn't work, but at that point you're way out of your league anyways. Supply and demand dictates that the watch will be worth more on the moon than on earth. Supply and demand dictates that the watch will be worth more on the moon than on earth.
  • 19. MacGyver I would then MacGyver my way out of the room using the shoelaces as a lockpick and the watch battery and wires from the watch as a makeshift taser to stun my captors, I'm not MacGyver. Think like MacGyver and use the shoelaces and the wristwatch to make a explosvie device to blow out one of the walls. What you can do with this information only having a cheap digital wristwatch and a pair of shoes in a room with no windows, and you are not MacGyver, then you're pretty much screwed. If you are MacGyver, you'll be fine. Einstein's equivalence principal also states that you can be in a spacecraft accelerating at a strength equivalent to either the earth or the moon and you wouldn't know from this information whither or not you were on the earth, the moon, or a spaceship. why figure out where you are when you could use your sweet McGyver skills and use these objects to make a small explosive with which you can escape!
  • 20.
  • 21.

Editor's Notes

  1. 1