1. University Physics: Waves and Electricity Ch15. Simple Harmonic Motion Lecture 1 Dr.-Ing. Erwin Sitompul http://zitompul.wordpress.com

2. 1/2 Erwin SitompulUniversity Physics: Waves and Electricity 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

3. 1/3 Erwin SitompulUniversity Physics: Waves and Electricity Grade Policy 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.

4. 1/4 Erwin SitompulUniversity Physics: Waves and Electricity Lecture Activities  The lectures will be held every Tuesday and Wednesday: 17:30 – 18:30 : Class 17:15 – 18:15 18:30 – 19:00 : Break18:15 – 18:45 19:00 – 20:45: Class18:45 – 20:30  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.

5. 1/5 Erwin SitompulUniversity 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 : 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.

6. 1/6 Erwin SitompulUniversity Physics: Waves and Electricity 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

7. 1/7 Erwin SitompulUniversity Physics: Waves and Electricity 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:

8. 1/8 Erwin SitompulUniversity Physics: Waves and Electricity Simple Harmonic Motion  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.

9. 1/9 Erwin SitompulUniversity Physics: Waves and Electricity 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.

10. 1/10 Erwin SitompulUniversity Physics: Waves and Electricity Simple Harmonic Motion

11. 1/11 Erwin SitompulUniversity 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 ? Checkpoint T 1.5T0.5T At +x m At –x m At 0 Between 0 and +x m

12. 1/12 Erwin SitompulUniversity Physics: Waves and Electricity 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:

13. 1/13 Erwin SitompulUniversity Physics: Waves and Electricity Plotting The Motion 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)

14. 1/14 Erwin SitompulUniversity Physics: Waves and Electricity Homework 1: Plotting the Motions 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)?