Unit 9 Vibrations and waves

Vibrations occur in: ______________________________________ 2. __________________________________ 3. ______________________________________ 4. ______________________________________ 5. ______________________________________ 6. ______________________________________ 7. ______________________________________ 8. ______________________________________ In addition, vibrations cause ___________ . Vibrations can be understood by using _____________________________ as models. Earth and Sun Vocal cords and eardrums radios, speakers, and motors atomic particles buildings and bridges musical instruments solids: steel, wood, glass liquids and gases waves pendulums and springs

that act on the pendulum bob at points A, B and C. Ex 1: Draw the forces that act on the pendulum bob at points A, B and C. A C B At A: At B: At C: T T T w w w In all 3 cases, Fnet ___________________. This must be true because ________________________________________ and so it is _______________________ . does not equal 0 the bob is changing speed and direction accelerating

The weight w can be ______________________________ : resolved into components q q This component is ______________ to the motion and is ____________ in direction to the ____________ perpendicular opposite w|| w|| tension w┴ w┴ w w equilibrium w|| is the part of w that is ______________________motion. w|| _______________ as q increases w|| pulls the bob back towards __________________ w|| is called a ___________________ force. parallel to the increases equilibrium restoring

Ex 2: Vibrating mass m on a spring with constant k: compression stretching x x spring m m x =0 equilibrium Draw the forces that act on the mass at the points shown: FN FN FS FS w w Except at x = 0, Fnet ____________________________ FS _________________ as x increases FS pulls the mass back towards __________________ FS is also a ______________________ force. does not equal zero increases equilibrium restoring

harmonic Simple _______________ motion (SHM): --vibrations in an ______________ material -- due to a restoring force that is __________ ____________________ to a displacement. elastic directly proportional SHM occurs because of ____________________ : Hooke's Law F = -kx From Newton's 2nd Law, we know that F = ______ ma ma = -kx the 2nd time derivative of x Calculus tells us that a = ___________________________: m d2x dt2 = -kx The solutions to this equation are _____________________ sines and cosines

sine ______ curve: x time cosine ______ curve: x time T the period of vibration T = ________________________ Both of these curves are ______________ and describe the __________________________ that is ___________________________________________. periodic motion of an object vibrating in simple harmonic motion

period T: the time for _________________________________ SI unit for T: _______________ one complete cycle or vibration seconds, s Ex: It takes a pendulum 40 seconds to complete 10 complete back and forth swings (10 cycles). What is its period? 40 s T = = 4 s 10 "cycles"  Notice that ______________ is ignored as a unit. # of complete cycles that occur frequency f: f = time Ex: Find the frequency of vibration for the above example. 10 f = 0.25 = 40 s s

Other ___________ can be used for T and f. But when the time is in _______________ , the unit for frequency is: units seconds (s) 1 or s-1 s This unit is called a _____________ It is _____________ from the fundamental unit ____ . So the answer to the last example can be written: hertz, Hz. derived s f = 0.25 s-1 = 0.25 Hz Notice: T = f = 4 s 0.25 s-1 = ¼ s-1 From this example, it can be seen that period and frequency are _____________ : T = 1 f inverses