University Physics: Waves and Electricity

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

2. Textbook and Syllabus Textbook: “Fundamentals of Physics”, Halliday, Resnick, Walker, John Wiley & Sons, 8th 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 University Physics: Waves and Electricity

3. 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. University Physics: Waves and Electricity

4. 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 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. University Physics: Waves and Electricity

5. 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. University Physics: Waves and Electricity

6. 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 University Physics: Waves and Electricity

7. Simple Harmonic Motion • Related to the frequency is the periodT 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: University Physics: Waves and Electricity

8. 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. University Physics: Waves and Electricity

9. 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. University Physics: Waves and Electricity

10. Simple Harmonic Motion University Physics: Waves and Electricity

11. 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 = 2T (b) t = 3.5T (c) t = 5.25T (d) t = 2.8T ? At +xm At –xm At 0 Between 0 and +xm 0.5T 1.5T T University Physics: Waves and Electricity

12. 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: University Physics: Waves and Electricity

13. xm xm xm 0 0 0 0.5T 0.5T 0.5T T T T –xm –xm –xm Plotting The Motion Plot the following simple harmonic motions: (a) x1(t) = xmcosωt (b) x2(t) = xmcos(ωt+π) (c) x3(t) = (xm/2)cosωt (d) x4(t) = xmcos2ωt x1(t) x2(t) x1(t) x3(t) x1(t) x4(t) University Physics: Waves and Electricity

14. xm xm xm 0 0 0 0.5T 0.5T 0.5T T T T –xm –xm –xm Homework 1: Plotting the Motions Plot the following simple harmonic motions in three different plots: (a) xa(t) = xmcosωt (b) xb(t) = xmcos(ωt–π/2) (c) xc(t) = xm/2cos(ωt+π/2) (d) xd(t) = 2xmcos(2ωt+π) xa(t) xb(t)? xa(t) xc(t)? xa(t) xd(t)? University Physics: Waves and Electricity