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Waves Physics 202 Professor Lee Carkner Lecture 5
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PAL #4 Pendulums The initial kinetic energy is just the kinetic energy of the bullet The initial velocity of the block comes from the kinetic energy KE = ½mv 2 Amplitude =x m, can get from total energy Initial KE = max KE = total E = ½kx m x m =(2E/k) ½ = ([(2)(1250)]/(5000)) ½ = 0.71 m Equation of motion = x(t) = x m cos( t) k = m 2 x(t) = 0.71 cos(31.6t)
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Test Next Friday About 15 multiple choice Like Quizdom About 4 problems Like PALs or homework Bring calculator and pencil Formulas and constants provided (but not labeled) Worth 10% of grade I have put practice problems on webassign Not for grade
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Transverse Waves Examples: waves on a string, ocean waves Sometimes called shear waves
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Longitudinal Waves Examples: slinky, sound waves Sometimes called pressure waves
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Waves Properties The wave has a net displacement but the medium does not The y position is a function of both time and x position and can be represented as: y(x,t) = y m sin (kx- t) Where: k = angular wave number = angular frequency
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Wavelength and Number One wavelength must include a maximum and a minimum and cross the x-axis twice We will often refer to the angular wave number k, k=
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Period and Frequency Frequency is the number of oscillations (wavelengths) per second (f=1/T) =2 /T The quantity (kx- t) is called the phase of the wave
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Speed of a Wave y(x,t) = y m sin (kx- t) But we want to know how fast the waveform moves along the x axis: v=dx/dt If we wish to discuss the wave form (not the medium) then y = constant and: kx- t = constant we want to know how fast the peak moves
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Wave Speed
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Velocity k(dx/dt) - = 0 (dx/dt) = /k = v Since = 2 f and k = v = /k = 2 f /2 v = f i.e. v is the velocity of the wave form
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Next Time Read: 16.6-16.10
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If the amplitude of a linear oscillator is doubled, what happens to the period? a)Quartered b)Halved c)Stays the same d)Doubled e)Quadrupled
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If the amplitude of a linear oscillator is doubled, what happens to the spring constant? a)Quartered b)Halved c)Stays the same d)Doubled e)Quadrupled
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If the amplitude of a linear oscillator is doubled, what happens to the total energy? a)Quartered b)Halved c)Stays the same d)Doubled e)Quadrupled
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If the amplitude of a linear oscillator is doubled, what happens to the maximum velocity? a)Quartered b)Halved c)Stays the same d)Doubled e)Quadrupled
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If the amplitude of a linear oscillator is doubled, what happens to the maximum acceleration? a)Quartered b)Halved c)Stays the same d)Doubled e)Quadrupled
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If you have a pendulum of fixed mass and length and you increase the length of the path the mass travels, what happens to the period? a)Increase b)Decrease c)Stay the same
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If you have a pendulum of fixed mass and length and you increase the length of the path the mass travels, what happens to the maximum velocity? a)Increase b)Decrease c)Stay the same
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If you have a pendulum of fixed mass and length and you increase the length of the path the mass travels, what happens to the maximum acceleration? a)Increase b)Decrease c)Stay the same
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