University Physics: Waves and Electricity Ch15. Simple Harmonic Motion Lecture 1 Dr.-Ing. Erwin Sitompul

1/2 Erwin Sitompul University Physics: Waves and Electricity Textbook and Syllabus Textbook: “Fundamentals of Physics”, Halliday, Resnick, Walker, John Wiley & Sons, 8 th Extended, 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

1/3 Erwin Sitompul University Physics: Waves and Electricity 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 A4 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.

1/4 Erwin Sitompul University Physics: Waves and Electricity Grade Policy  Extra points will be given if you solve a problem in front of the class. You will earn 1, 2, or 3 points.  Make up of quizzes and exams will be held one week after the schedule of the respective quizzes and exams.  The score of a make up quiz or exam, upon discretion, can be multiplied by 0.9 (the maximum score for a make up is 90). Heading of Homework Papers (Required) Physics 2 Homework 5 Rudi Bravo March 2021 No.1. Answer:

1/5 Erwin Sitompul University Physics: Waves and Electricity Lecture Activities  The lectures will be held every Wednesday: 18:30 – 21:00 with 15 minutes break if required  Lectures will be held in the form of PowerPoint 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. Do the homeworks by yourself Solve problems in front of the class Take time to learn at home Ask questions How to get good grades in this class?

1/6 Erwin Sitompul University Physics: Waves and Electricity Lecture Material  New lecture slides will be available on internet every Thursday afternoon. Please check the course homepage regularly.  The course homepage is :  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.

1/7 Erwin Sitompul University Physics: Waves and Electricity  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 Simple Harmonic Motion

1/8 Erwin Sitompul University Physics: Waves and Electricity  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: Simple Harmonic Motion

1/9 Erwin Sitompul University Physics: Waves and Electricity  This motion is called simple harmonic motion (SHM).  Means, the periodic motion is a sinusoidal function of time.  The quantity x m 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 ±x m. Simple Harmonic Motion

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

1/11 Erwin Sitompul University Physics: Waves and Electricity Simple Harmonic Motion

1/12 Erwin Sitompul University Physics: Waves and Electricity A particle undergoing simple harmonic oscillation of period T is at x m at time t = 0. Is it at –x m, at +x m, at 0, between –x m and 0, or between 0 and +x m when: (a) t = 2T (b) t = 3.5T (c) t = 5.25T (d) t = 2.8T ? T 1.5T0.5T At +x m At –x m At 0 Between 0 and +x m Checkpoint

1/13 Erwin Sitompul University Physics: Waves and Electricity  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: Velocity and Acceleration of SHM

1/14 Erwin Sitompul University Physics: Waves and Electricity Plot the following simple harmonic motions: (a) x 1 (t) = x m  cosωt (b) x 2 (t) = x m  cos(ωt+π) (c) x 3 (t) = (x m /2)  cosωt (d) x 4 (t) = x m  cos2ωt x1(t)x1(t) T0.5T xmxm –x m 0 x2(t)x2(t) x1(t)x1(t) T0.5T xmxm –x m 0 x3(t)x3(t) x1(t)x1(t) T0.5T xmxm –x m 0 x4(t)x4(t) Plotting The Motion

1/15 Erwin Sitompul University Physics: Waves and Electricity Plot the following simple harmonic motions in three different plots: (a) x a (t) = x m  cosωt (b) x b (t) = x m  cos(ωt–π/2) (c) x c (t) = x m /2  cos(ωt+π/2) (d) x d (t) = 2x m  cos(2ωt+π) xa(t)xa(t) T0.5T xmxm –x m 0 x b (t)? xa(t)xa(t) T0.5T xmxm –x m 0 x c (t)? xa(t)xa(t) T0.5T xmxm –x m 0 x d (t)? Homework 1: Plotting the Motions

1/16 Erwin Sitompul University Physics: Waves and Electricity New Homework 1: Plotting the Motions Plot the following simple harmonic motions in three different plots: (a) x a (t) = x m  sinωt (b) x b (t) = x m  sin(ωt–π) (c) x c (t) = x m /2  sin(ωt+π/2) (d) x d (t) = x m /2  sin(2ωt+π/2)