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LCcircuit

Course: RPK 101, Fall 2009
School: Uni. Worcester
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Word Count: 172

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ANALOGY MASS-SPRING MECHANICAL-ELECTRICAL SYSTEM Displacement x Velocity Diff Eqn: dx =v dt d 2x m 2 + kx = 0 dt LC CIRCUIT Charge q Current Diff Eqn: dq =i dt d 2q 1 L 2 + q=0 dt C Mass m Spring constant k Frequency = k m Inductance L Inverse Capacitance 1 / C Frequency = 1 LC Displacement: x = A cos (t + ) Velocity: v = A sin (t + ) Potential energy U = kx 2 = m 2 x 2 1 2 1 Kinetic energy K = mv 2 2 1...

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ANALOGY MASS-SPRING MECHANICAL-ELECTRICAL SYSTEM Displacement x Velocity Diff Eqn: dx =v dt d 2x m 2 + kx = 0 dt LC CIRCUIT Charge q Current Diff Eqn: dq =i dt d 2q 1 L 2 + q=0 dt C Mass m Spring constant k Frequency = k m Inductance L Inverse Capacitance 1 / C Frequency = 1 LC Displacement: x = A cos (t + ) Velocity: v = A sin (t + ) Potential energy U = kx 2 = m 2 x 2 1 2 1 Kinetic energy K = mv 2 2 1 2 121 2 kx + mv = const 2 2 Charge: q = Q cos (t + ) Current: = i Q sin (t + ) Electrical energy Magnetic energy q2 1 = CV 2 2C 2 12 Li 2 q2 1 2 + Li = const 2C 2 See Fig.30.15 of the text for a diagram of an LC circuit. The arrow in the figure shows the arbitrary direction chosen for a positive current. By convention, a current flowi...

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Uni. Worcester - RPK - 101
The damped harmonic oscillatorConsider a mass-spring system with a mass m attached to a spring of constant k . If the mass is displaced from its equilibrium position and released, it will oscillate with the frequency 0 = k / m (note that I have atta
Uni. Worcester - RPK - 101
The forced, damped harmonic oscillatorThe differential equation for a forced, damped oscillator is d 2x dx m 2 + b + kx = F0 cos (t ) dt dt or d 2x dx 2 + + 0 x = f 0 cos (t ) 2 dt dt (1)0 =F k b , = , f0 = 0 m m mAfter the transients have di
Uni. Worcester - RPK - 101
SOUND WAVESSound waves are longitudinal waves in a medium Speed of sound in air at 20C = 344m/s Audible sound: 20Hz 20kHz Sound speed = Frequency x Wavelength: v = f Displacement for a sound wave traveling along the +x direction:2 2 y ( x, t )
Uni. Worcester - RPK - 101
PH1140E2009 : Oscillations and Waves Objectives LECTURE-1( Tuesday, May 26, 2009)After the completion of this lecture, you will be able to 1. describe the oscillations in terms of amplitude, period, frequency, and angular frequency, 2. add two or
Uni. Worcester - RPK - 101
PH1140E09Solutions (Suggested problems-1)May 29, 2009End-of-the-Chapter-Suggested problems 13.3 Number of complete vibrations made by the fork tip, (n) = 440, time (t) = 0.500s,gives the frequency, (f ) = n/t = 880Hz . Therefore, the angular
Uni. Worcester - RPK - 101
PH1140E2009 : Oscillations and Waves Objectives LECTURE-2( Wednesday, May 27, 2009)After completion of this lecture, you will be able to 1. analyze an SHM using energy concepts and 2. analyze the motions of a simple pendulum. We will cover the f
Uni. Worcester - RPK - 101
PH1140E09Solutions (Suggested problems-2)May 29, 2009End-of-the-Chapter-Suggested problems 13.23 The mass of the glider, (m) = 0.500 kg , the force constant of the spring,(k ) = 450 N/m, and amplitude of an SHM, (A) = 0.040 m. Therefore, the
Uni. Worcester - RPK - 101
PH1140E2009 : Oscillations and Waves Objectives After completion of this lecture, you will be able toLECTURE-3(Friday, May 29, 2009)1. relate the induced emf in a circuit to the rate of change current in the same circuit, 2. calculate the energy
Uni. Worcester - RPK - 101
PH1140E09Solutions (Suggested problems-3)June 3, 2009End-of-the-Chapter-Suggested problems 13.56 The mass of an object, (m) = 2.20 kg , the force constant of the spring,(k ) = 250 N/m, and the period of oscillation, (T ) = 0.615 s. (a) The a
Uni. Worcester - RPK - 101
PH1140E2009 : Oscillations and Waves Objectives After completion of this lecture, you will be able toLECTURE-4(Monday, June 01, 2009)1. solve the problems in a forced, damped oscillating mass-spring system and 2. explain the condition for resona
Uni. Worcester - RPK - 101
PH1140E09Solutions (Suggested problems-4)May 29, 2009End-of-the-Chapter-Suggested problems 13.60 The force constant of a forced, damped harmonic oscillator = k and mass =0 0 0 2m. The damping constant, (b) = b1 and amplitude = A1 . The
Uni. Worcester - RPK - 101
PH1140E2009 : Oscillations and Waves Objectives LECTURE-5(Wednesday, June 03, 2009)After completion of this lecture, you will be able to 1. solve the problems in the driven L-C-R circuits, and 2. explain the condition for resonance of an electric
Uni. Worcester - RPK - 101
PH1140E09 Additional problemsSolutions (Suggested problems-5)May 29, 20091. An L-C-R circuit with self-inductance of 0.01 H is described by 0.01 d2 q dq + 10 + 5 105 q = 0.5 cos(5000 t). 2 dt dt (1)To solve this problem, we compare this equa
Uni. Worcester - RPK - 101
PH1140E2009 : Oscillations and Waves Objectives After completion of this lecture, you will be able to 1. describe a mechanical wave, 2. solve problems using wave equation: v = f , andLECTURE-6 (Monday, June 08, 2009)3. describe the waves on a st
Uni. Worcester - RPK - 101
PH1140E09Solutions (Suggested problems-6)May 29, 2009End-of-the-Chapter-Suggested problems 15.6 The given transverse wave equation: y (x, t) = (6.50 mm) cos 2 t x 28.0 cm 0.0360 sA comparison of this equation to the standard transverse wave
Uni. Worcester - RPK - 101
PH1140E2009 : Oscillations and Waves Objectives LECTURE-7 (Wednesday, June 10, 2009)After completion of this lecture, you will be able to 1. calculate the speed of transverse waves on a stretched rope or string, and 2. calculate the energy transp
Uni. Worcester - RPK - 101
PH1140E09Solutions (Suggested problems-7)May 29, 2009End-of-the-Chapter-Suggested problems 15.14 The length of the rope, (l) = 2.50 m and mass of the rope, (m) = 0.120 kg . Thefrequency of a transverse wave to be set up on the string, (f ) =
Uni. Worcester - RPK - 101
PH1140E2009 : Oscillations and Waves Objectives After completion of this lecture, you will be able toLECTURE-8 (Friday, June 12, 2009)1. explain how standing waves are formed on a stretched rope or string, 2. analyze the standing waves on a stri
Uni. Worcester - RPK - 101
PH1140E09Solutions (Suggested problems-8)May 29, 2009End-of-the-Chapter-Suggested problems 15.33 The standing waves on a wire are described by y (x, t) = (ASW sin kx) sin t. The amplitude of the standing wave, (ASW ) = 2.50 mm = 2.50 103 m, t
Uni. Worcester - RPK - 101
PH1140E2009 : Oscillations and Waves Objectives After completion of this lecture, you will be able toLECTURE-9 (Monday, June 15, 2009)1. describe a sound wave in terms particle displacements or pressure uctuations, 2. calculate the speed of soun
Uni. Worcester - RPK - 101
PH1140E09Solutions (Suggested problems-9)May 29, 2009End-of-the-Chapter-Suggested problems 16.3 The displacement amplitude, (A) = 0.02 mm = 2.00 105 m. The adia-batic bulk modulus of air, (B ) = 1.42 105 P a.(a) The frequency of the soun
Uni. Worcester - RPK - 101
PH1140E2009 : Oscillations and Waves Objectives LECTURE-10 (Thursday, June 18, 2009)After completion of this lecture, you will be able to 1. describe the resonance in sound, 2. describe interference of two sound waves, and 3. describe the formati
Uni. Worcester - RPK - 101
PH1140E09Solutions (Suggested problems-10)May 29, 2009End-of-the-Chapter-Suggested problems 16.31 The length of the air column in the test tube, (l) = 14.0 cm = 0.140 m, and thespeed of sound, (v ) = 344 m/s. (a) The test tube acts as a clos
Uni. Worcester - RPK - 101
PH1140E2009 : Oscillations and Waves Objectives After completion of this lecture, you will be able toLECTURE-11 (Monday, June 22, 2009)1. explain why the pitch of sound rises and falls when there is a relative motion between a source and an obse
Uni. Worcester - RPK - 101
PH1140E09Solutions (Suggested problems-11)May 29, 2009End-of-the-Chapter-Suggested problems 16.41 In this problem, the male ornithoid is the source of sound and the female is thelistener. The speed of the male ornithoid, (vS ) = 25.0 m/s. Th
Uni. Worcester - RPK - 101
PH1140E09Homework-2 (Due : Thursday, May 28, 2009)May 21, 2009Please read the Homework Rules and submit the solution accordingly. 1. Let z =2ej/6 . 43jCalculate the following quantities in three signicant gures.(a) The real part of z . (b)
Uni. Worcester - RPK - 101
PH1140E09Homework-2 (Due : Thursday, May 28, 2009) - SOLUTION May 29, 20092ej/6 . 43j1. The given complex number, z =First, lets express this in the form : z = x + jy , where x is the real part of z , y is its ej/6 imaginary part and j = 1. U
Uni. Worcester - RPK - 101
PH1140E09Homework-4 (Due : Tuesday, June 02, 2009)May 21, 2009Please read the Homework Rules and submit the solution accordingly. 1. You are asked to design an L-C circuit with a frequency of 5000Hz for a particular application. The maximum val
Uni. Worcester - RPK - 101
PH1140E09Homework-4 (Due : Tuesday, June 02, 2009) - SOLUTIONMay 21, 20091. The oscillation frequency of an L-C circuit, (f ) = 5000 Hz , the maximum voltage across the capacitor, (Vmax ) = 25.0 V and the maximum energy stored in the capacitor,
Uni. Worcester - RPK - 101
PH1140E09Homework-7 (Due : Thursday, June 11, 2009)May 21, 2009Please read the Homework Rules and submit the solution accordingly. 1. (Problem 15.4, 12th Ed.) Sound having frequencies above the range of humanhearing ( about 20, 000 Hz ) is ca
Uni. Worcester - RPK - 101
PH1140E09Homework-7 (Due : Thursday, June 11, 2009) - SOLUTION May 21, 20091. (Problem 15.4, 12th Ed.) The wavelength of an ultrasound, () = 1.00 mm = 1.00 103 m, and its speed through the body tissue, (v ) = 1500 m/s. The frequency of the sound
Uni. Worcester - RPK - 101
PH1140E09Homework-8 (Due : Monday, June 15, 2009)May 21, 2009Please read the Homework Rules and submit the solution accordingly. 1. (Problem 15.34, 12th Ed.) Adjacent antinodes of a standing wave on a string are 15.0 cm apart. A particle at an
Uni. Worcester - RPK - 101
PH1140E08Homework-8 (Due : Monday, June 15, 2009) - SOLUTIONJune 16, 20091. (Problem 15.34, 12th Ed.) a half wavelength, 2Since the adjacent antinodes are separated by= 15.0 cm = 0.150 m, which gives the wavelength, () = 0.300 m.The ampl
Uni. Worcester - RPK - 101
HW#8: June 15, 2009 (a) At t = 0 s,(b) At t = 500 s(c) At t = 1 msThe above sketches show the shapes of a string (carrying a wave from right to left) at times t = 0.000 s, t = 500s and t = 1.00 m s respectively.
Uni. Worcester - RPK - 101
PH1140E09Homework-11 (Due : Tuesday, June 23, 2009)May 21, 2009Please read the Homework Rules and submit the solution accordingly. 1. Two organ pipes, both closed at one end and open at the other, have lengths of 0.98 m and 1.00 m. (a) Calculat
Uni. Worcester - RPK - 101
Phase, Oscillations and Trig Functions The standard form of an oscillation is x = A cos (t + ) , where the amplitude A is a positive quantity and the initial phase is an angle between 0 and 2 radians. Below are several problems that allow you to un
Uni. Worcester - RPK - 101
PH1140E09SOLUTIONS (All Suggested Problems )June 3, 2009Course : Physics - 1140 ( Oscillations and Waves, Term E, 2009) Text Book : University Physics, 12th Edition by Young and Freedman Instructor : Rudra Kae , Physics Department, WPI, MA NOT
Uni. Worcester - RPK - 101
PH1140E09PRACTICE EXAM -1May 21, 2009PHYSICS - 1140 : OSCILLATIONS AND WAVESName: Time : 4:30 P.M.- 5:30 P.M.INSTRUCTIONS: 1. The only reference material you may use is one 8 1 11 crib sheet and a calculator. 2 2. Show your work clearl
Uni. Worcester - RPK - 101
PH1140E09PRACTICE EXAM -1: SOLUTIONMay 21, 2009PHYSICS - 1140 : OSCILLATIONS AND WAVESName: Time : 4:30 P.M.- 5:30 P.M.INSTRUCTIONS: 1. The only reference material you may use is one 8 1 11 crib sheet and a calculator. 2 2. Show your w
Uni. Worcester - RPK - 101
PH1140E09Practice Exam-2May 21, 2009PHYSICS - 1140 : OSCILLATIONS AND WAVESName: Time : 4:30 P.M.- 5:30 P.M.INSTRUCTIONS: 1. The only reference material you may use is one 8 1 11 crib sheet. 2 2. You will need a calculator for the exam
Uni. Worcester - RPK - 101
PH1140E09Practice Exam-2: SOLUTIONJune 16, 2009PHYSICS - 1140 : OSCILLATIONS AND WAVESName: Time : 4:30 P.M.- 5:30 P.M.INSTRUCTIONS: 1. The only reference material you may use is one 8 1 11 crib sheet. 2 2. You will need a calculator fo
Uni. Worcester - RPK - 101
PH1140E09Practice Exam-3May 21, 2009PHYSICS - 1140 : OSCILLATIONS AND WAVESName: Time : 4:30 P.M.- 5:30 P.M.INSTRUCTIONS: 1. The only reference material you may use is one 8 1 11 crib sheet. 2 2. You will need a calculator for the exam
Uni. Worcester - RPK - 101
PH1140E2009STUDY GUIDE -1Instructor : Rudra KaePHYSICS - 1140 : Oscillations and Waves, TERM - E , 2009 TEXT-BOOK : University Physics - Young and Freedman, 12th Edition Objectives 1. Describe the oscillations in terms of amplitude, period, f
Uni. Worcester - RPK - 101
PH1140E2009STUDY GUIDE -2Instructor : Rudra KaePHYSICS - 1140 : Oscillations and Waves, TERM - E , 2009 TEXT-BOOK : University Physics - Young and Freedman, 12th Edition Objectives 1. Describe a mechanical wave. 2. Solve problems using wave e
Uni. Worcester - RPK - 101
PH1140E2009STUDY GUIDE - 3Instructor : Rudra KaePHYSICS - 1140 : Oscillations and Waves, TERM - E , 2009 TEXT-BOOK : University Physics - Young and Freedman, 12th Edition Objectives 1. Describe the resonance in sound. 2. Describe interference
Uni. Worcester - RPK - 101
PH1140E09EXAM - 1: SOLUTIONJune 5, 2009PHYSICS - 1140 : OSCILLATIONS AND WAVESName: Time : 4:30 P.M. - 5:30 P.M.INSTRUCTIONS: 1. The only reference material you may use is one 8 1 11 crib sheet and a calculator. 2 2. Show your work clea
Uni. Worcester - RPK - 101
PH1140E09Exam-2 : SOLUTIONJune 17, 2009PHYSICS - 1140 : OSCILLATIONS AND WAVESName: Time : 4:30 P.M. - 5:30 P.M.INSTRUCTIONS: 1. The only reference material you may use is one 8 1 11 crib sheet. 2 2. You will need a calculator for the e
Uni. Worcester - RPK - 101
PH1140E09: Oscillations and Waves RUDRA KAFLE T D MROUTINE [TERM E, 2009]1:30P.M. -3:00P.M. OH3:00P.M. 4:00P.M.4:30P.M. -5:30 P.M. PH-1140 (Lecture) (OH-218)TOHPH-1140 (Labs) (OH-117)PH-1140 (Conference) (OH-218)WOHTH OH PH-114
Uni. Worcester - RPK - 101
PHYSICS-1140: Oscillations and Waves Term-E, 2008 (May 27- June 26) Lecturer: Rudra Kafle Lecture Hall : OH-126 Time: 11: 45 AM - 12: 55 PM Textbook: Young and Freedman, University Physics, 12th Ed. (Addison Wesley, 2007). The schedule of lecture top
Uni. Worcester - RPK - 101
PHYSICS-1140: Oscillations and Waves Homework Rules!Term-E, 2008 (May 27- June 26)1. Give all numerical answers in THREE SIGNIFICANT FIGURES. One point is deducted otherwise! 2. Express the angles in degrees only up to ONE PLACE after the decimal
Uni. Worcester - RPK - 101
PHYSICS-1140: Oscillations and WavesTerm-E, 2008 (May 27- June 26)LABORATORY INFORMATION AND RULES Lab Instructor : Rudra P. Kafle Office : OH-114 E-mail : rpk101@wpi.edu Web-page: http:/users.wpi.edu/~rpk101/PH1140E08.html Office Phone : 508-831
N.C. State - MA - 584
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N.C. State - MA - 584
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N.C. State - MA - 584
N.C. State - MA - 584
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