PHY131H1F - Class 20. Today: Today, Chapter 13: General Periodic Oscillations. Special case: Simple Harmonic Motion

Transcription

1 Today: Today, Chapter 13: General Periodic Oscillations Special case: Simple Harmonic Motion PHY131H1F - Class 20 Animation from

2 A construction worker of mass m w sits 2.0 m from the end of a steel beam of mass m b, as shown. The tension in the Cable is T The wall exerts a normal force, n on the beam, and an upward force, F 1. Define +x = to the right, +y = up, and the pivot is the point where the beam touches the wall. F 1n What is the normal force, n? A. (m b + m w )g B. (m b + m w )g T cos(30 ) C. (m b + m w )g T sin(30 ) D. T sin(30 ) E. T cos(30 ) 6.0 m m w g m b g T

3 A construction worker of mass m w sits 2.0 m from the end of a steel beam of mass m b, as shown. The tension in the Cable is T The wall exerts a normal force, n on the beam, and an upward force, F 1. Define +x = to the right, +y = up, and the pivot is the point where the beam touches the wall. What is the force, F 1? F 1n A. (m b + m w )g m w g m b g B. (m b + m w )g T cos(30 ) C. (m b + m w )g T sin(30 ) D. T sin(30 ) E. T cos(30 ) 6.0 m T

4 Class 20 Preclass Quiz on MasteringPhysics This was due this morning at 8:00am 91% of students got: What term denotes the time for one cycle of a periodic process? Period. 96% of students got: For vibrational motion, what term denotes the maximum displacement from the equilibrium position? Amplitude. 93% of students got: A mass on the end of a spring undergoes simple harmonic motion. At the instant when the mass is at its maximum displacement from equilibrium, its instantaneous velocity is zero.

5 Class 20 Preclass Quiz Student Comments i miss those simple days were the only physics you had to know was speed=distance/time. What is the force on the mass at the equallibrium point? Harlow answer: zero. Equilibrium is defined as F net = 0. If the mass was at rest there, it would stay at rest. What's the difference between period and wavelength? Harlow answer: Period is the distance between crests on a plot of y vs t (sometimes called a history graph ), and wavelength is the distance between crests on a plot of y vs x (sometimes called a snapshot graph ). Anything that is oscillating has a period, but only waves have wavelength. i always used to play with rulers on the edge of the table as a kid and it annoyed everyone, so that example in the book really spoke to me.

6 Class 20 Preclass Quiz Student Comments My confidence level in this course can be modelled as a periodic function. The crests (max confidence) occur right before a term test and the troughs (min confidence) occur once the marks are given back. I still did pretty badly on the Physics test, but I improved 6.5 points from last time, and my dad told me he was proud of me, so I am taking this as a victory. GUYS DO THE COURSE EVALUATION k thanks Ummmm...Do we need to know how to make spreadsheets for the final, cuz...well...seems kind of difficult? Harlow answer: No. There won t be any spreadsheet questions on the final exam; I was just doing that in the video to conceptually explain simple harmonic motion.

7 You should now see your mark out of 32 under My Grades on portal. The raw average was 19/32 = 59%. The instructors in this course have decided to adjust the marks by adding 3 points to every student s mark, but holding the maximum mark to 32/32 = 100%. Test 2 Marks Posted The mark posted on portal is your adjusted mark. The adjusted average and median were 22/32 = 69%. After the adjustment, 185 students (20% of the class) got less than 16/32 (fail). After the adjustment, 77 students (8% of the class) got 32/32 = 100%.

8 Test 2 Marks Posted You will receive the long-answer part of your test in Practicals between today and Dec. 1. The multiple choice bubble sheet is stored in MP129 if you would like to review it, please stop by and ask April. Check over the marking and compare it to the Test 2 Marking Scheme posted on the portal. If there has been a mistake in the marking or computation of your mark, please bring the test to me or April Seeley in MP129 and we will fix the mistake. The deadline to report mistakes in the marking of Test 1 is Dec. 9.

9 Class 20 Preclass Quiz Student Comments I have a Chem midterm today, so wish me luck :) Harlow response: Good luck to all CHM138 students on tonight s test! The last problem set was due to Tuesday which was different than all others which were due to Monday :( This significantly conflicted my weekly schedule! I wish they were due to Friday like the beginning of semester! Why the deadline has changed three times? Harlow answer: They are always right after a full cycle of practicals you are meant to be studying in Practicals to do well on the problem set. They are posted 1.5 weeks in advance so if you want to keep doing them on Friday nights that is okay.

10 Class 20 Preclass Quiz Student Comments I HAVE BEEN SAYING THIS FOR THE PAST 4 PRE-QUIZ COMMENTS. YOU LOOK LIKE JUSTIN TRUDEAU please, I am losing hope on humanity... could you please post this on the powerpoint... I don't want to get out of this class with such grudge and regret.. That moment when seeing your comment on the screen makes you happier than passing this course would.. Just out of curiosity, in your university life, what was your biggest headache, physics? Harlow answer: No. I liked physics, even though it was hard, I never dreaded the work. My biggest headache was ENG100 Effective Writing. In retrospect it was an excellent course, but I was not ready, and I really hated it. To tell you the truth when the drop-date came I dropped it.

11 Bonus Point for Over 65% Course Evaluation Response Rate An essential component of my commitment to teaching excellence is the regular evaluation of courses by students. On Nov. 23 you were sent an by to evaluate PHY131H1F. It only takes 10 or 15 minutes to answer the questions and enter your typed thoughts about the course. Your answers and thoughts are anonymous, but are very important to me. I promise you that when the results become available to me in January, I will read every comment and scrutinize the responses to see if it can help me improve the course or my teaching in the future.

12 Bonus Point for Over 65% Course Evaluation Response Rate The end of the evaluation period for this semester is Thursday December 10 at 11:59PM. If, by the end of the course evaluation period, at least 65.00% of the students enrolled in this course have completed the course evaluations, then every student in the course will have 1% bonus added to their final course mark. If fewer than 65.00% of students complete the course evaluations by the deadline, then no bonus point will be added for any student. Results so far (as of 3:15pm today): Invited: Responded: 940 students 252 students Response Rate: 26.81%

13 Last day I asked A spring with a mass attached to it is stretched and released. When the spring returns to equilibrium, is the mass moving? Answer: Yes! It is not accelerating, but it is moving at that moment. Inertia then carries it past equilibrium to the other side. After passing equilibrium, the acceleration is opposite the velocity, so it slows down, eventually turning around. Equilibrium is at x = 6 in this animation.

14 Some oscillations are not sinusoidal:

15 Period, frequency, angular frequency The time to complete one full cycle, or one oscillation, is called the period, T. The frequency, f, is the number of cycles per second. Frequency and period are related by The oscillation frequency f is measured in cycles per second, or Hertz. We may also define an angular frequency ω in radians per second, to describe the oscillation.

16 The Spring-Mass System The force exerted on the mass by the spring: F = k x (Hooke s Law) F = m a (Newton s Second Law) Combine to form a differential equation: a d 2 dt x 2 k m x

17 The Spring-Mass System a 2 d x dt 2 k m x

18 F s kx a F m Net a x k m x

19 Simple Harmonic Motion If the initial position of an object in SHM is not A, then we may still use the cosine function, with a phase constant ϕ 0 measured in radians. In this case, the two primary kinematic equations of SHM are:

20 Simple Harmonic Motion (SHM) x Acos( t ) 0 v dx dt A sin( t 0) a dv dt 2 d x 2 dt 2 A cos( t 0)

21 A. Velocity is positive; force is zero. B. Velocity is negative; force is zero. C. Velocity is negative; force is to the right. D. Velocity is zero; force is to the right. E. Velocity is zero; force is to the left. This is the position graph of a mass on a spring. What can you say about the velocity and the force at the instant indicated by the dotted line?

22 A. Velocity is positive; force is zero. B. Velocity is negative; force is zero. C. Velocity is negative; force is to the right. D. Velocity is zero; force is to the right. E. Velocity is zero; force is to the left. This is the position graph of a mass on a spring. What can you say about the velocity and the force at the instant indicated by the dotted line?

23 What is ϕ 0? x Acos( t 0 ) A. π/3 B. +π/3 C. 2π/3 D. +2π/3 E. 0

24 S.H.M. notes. The frequency, f, is set by the properties of the system. In the case of a mass m attached to a spring of spring-constant k, the frequency is always f 1 2 A and ϕ 0 are set by the initial conditions: x 0 (initial position) and v 0 (initial velocity). A turns out to be related to the total energy of the spring oscillator system: E = ½ k A 2. k m

25 Clicker question Which of the following quantities in the description of simple harmonic motion is not determined by the initial position and velocity of the mass? A. the amplitude, A B. the phase constant, ϕ 0 C. the angular frequency, ω

26 A mass is oscillating on a spring in S.H.M. When it passes through its equilibrium point, an external kick suddenly decreases its speed, but then it continues to oscillate. As a result of this slowing, the frequency of the oscillation A. goes up B. goes down C. stays the same

27 Vertical Mass on a Spring

28 Vertical Mass on a Spring

29 Before Class 21 on Monday Please finish reading Chapter 13 on Oscillations. Problem Set 9 on Chapters is due Tuesday Dec.1 at 11:59pm. Something to think about over the weekend: If you double the mass of a mass on a spring, how does this change the frequency? If you double the mass of a swinging pendulum, how does this change the frequency? What is the difference here?