Lecture 1 Ch 15 Simple Harmonic Motion University

Lecture 1 Ch 15. Simple Harmonic Motion University Physics: Waves and Electricity Dr. -Ing. Erwin Sitompul http: //zitompul. wordpress. com

Textbook and Syllabus Textbook: “Fundamentals of Physics”, Halliday, Resnick, Walker, John Wiley & Sons, 8 th Extended, 2008. Syllabus: (tentative) Chapter 15: Simple Harmonic Motion Chapter 16: Transverse Waves Chapter 17: Longitudinal Waves Chapter 21: Coulomb’s Law Chapter 22: Finding the Electric Field – I Chapter 23: Finding the Electric Field – II Chapter 24: Finding the Electric Potential Chapter 26: Ohm’s Law Chapter 27: Circuit Theory Erwin Sitompul University Physics: Waves and Electricity 1/2

Grade Policy: Final Grade = 5% Homework + 30% Quizzes + 30% Midterm Exam + 40% Final Exam + Extra Points § Homeworks will be given in fairly regular basis. The average of homework grades contributes 5% of final grade. § Homeworks are to be written on A 4 papers, otherwise they will not be graded. § Homeworks must be submitted on time. If you submit late, < 10 min. No penalty 10 – 60 min. – 40 points > 60 min. – 60 points § There will be 3 quizzes. Only the best 2 will be counted. The average of quiz grades contributes 30% of final grade. § Midterm and final exam schedule will be announced in time. § Make up of quizzes and exams will be held one week after the schedule of the respective quizzes and exams. Erwin Sitompul University Physics: Waves and Electricity 1/3

Lecture Activities § The lectures will be held every Tuesday and Wednesday: 17: 30 – 18: 30 : Class 17: 15 – 18: 15 18: 30 – 19: 00 : Break 18: 15 – 18: 45 19: 00 – 20: 45 : Class 18: 45 – 20: 30 § Lectures will be held in the form of Power. Point presentations. § You are expected to write a note along the lectures to record your own conclusions or materials which are not covered by the lecture slides. Erwin Sitompul University Physics: Waves and Electricity 1/4

Lecture Material § New lecture slides will be available on internet every Thursday afternoon. Please check the course homepage regularly. § The course homepage is : http: //zitompul. wordpress. com § You are responsible to read and understand the lecture slides. If there is any problem, you may ask me. § Quizzes, midterm exam, and final exam will be open-book. Be sure to have your own copy of lecture slides. § Extra points will be given if you solve a problem in front of the class. You will earn 1, 2, or 3 points. Erwin Sitompul University Physics: Waves and Electricity 1/5

Simple Harmonic Motion § The following figure shows a sequence of “snapshots” of a simple oscillating system. § A particle is moving repeatedly back and forth about the origin of an x axis. § One important property of oscillatory motion is its frequency, or number of oscillations that are completed each second. § The symbol for frequency is f, and its SI unit is the hertz (abbreviated Hz). 1 hertz = 1 Hz = 1 oscillation per second = 1 s– 1 Erwin Sitompul University Physics: Waves and Electricity 1/6

Simple Harmonic Motion § Related to the frequency is the period T of the motion, which is the time for one complete oscillation (or cycle). § Any motion that repeats itself at regular intervals is called periodic motion or harmonic motion. § We are interested here only in motion that repeats itself in a particular way, namely in a sinusoidal way. § For such motion, the displacement x of the particle from the origin is given as a function of time by: Erwin Sitompul University Physics: Waves and Electricity 1/7

Simple Harmonic Motion § This motion is called simple harmonic motion (SHM). § Means, the periodic motion is a sinusoidal function of time. § The quantity xm is called the amplitude of the motion. It is a positive constant. § The subscript m stands for maximum, because the amplitude is the magnitude of the maximum displacement of the particle in either direction. § The cosine function varies between ± 1; so the displacement x(t) varies between ±xm. Erwin Sitompul University Physics: Waves and Electricity 1/8

Simple Harmonic Motion § The constant ω is called the angular frequency of the motion. § The SI unit of angular frequency is the radian per second. To be consistent, the phase constant Φ must be in radians. Erwin Sitompul University Physics: Waves and Electricity 1/9

Simple Harmonic Motion Erwin Sitompul University Physics: Waves and Electricity 1/10

Checkpoint A particle undergoing simple harmonic oscillation of period T is at xm at time t = 0. Is it at –xm, at +xm, at 0, between –xm and 0, or between 0 and +xm when: (a) t = 2 T At +xm (b) t = 3. 5 T At –xm At 0 (c) t = 5. 25 T Between 0 and +xm (d) t = 2. 8 T ? 0. 5 T 1. 5 T T Erwin Sitompul University Physics: Waves and Electricity 1/11

Velocity and Acceleration of SHM § By differentiating the equation of displacement x(t), we can find an expression for the velocity of a particle moving with simple harmonic motion: § Knowing the velocity v(t) for simple harmonic motion, we can find an expression for the acceleration of the oscillating particle by differentiating once more: Erwin Sitompul University Physics: Waves and Electricity 1/12

Plotting The Motion Plot the following simple xm harmonic motions: 0 (a) x 1(t) = xm cosωt (b) x 2(t) = xm cos(ωt+π) –xm (c) x 3(t) = (xm/2) cosωt (d) x 4(t) = xm cos 2ωt x x 1(t) 0. 5 T T x 2(t) m 0 x 1(t) 0. 5 T T x 3(t) –xm xm 0 –xm Erwin Sitompul x 1(t) 0. 5 T T x 4(t) University Physics: Waves and Electricity 1/13

Homework 1: Plotting the Motions xm Plot the following simple harmonic motions in three different plots: 0 (a) xa(t) = xm cosωt (b) xb(t) = xm cos(ωt–π/2) –xm (c) xc(t) = xm/2 cos(ωt+π/2) xm (d) xd(t) = 2 xm cos(2ωt+π) 0 xa(t) 0. 5 T T xb(t)? xa(t) 0. 5 T T xc(t)? –xm xm 0 –xm Erwin Sitompul xa(t) 0. 5 T T xd(t)? University Physics: Waves and Electricity 1/14