W3
Simple Harmonic Motion
Embedded Files
Simple Harmonic Motion (Ch. 15)
Simple Harmonic Motion (Ch. 15)
Lectures
Lectures
Additional lectures (from Spring 2020) are linked at the bottom of the page.
Tue: Chapter 15 overview / pdf of notes
Thu: Discussion / pdf of notes
Example Videos
Example Videos
From TA Ian Chaffey.
Reminder: TA office hours are on Friday at 1pm, please find the link pinned to the #general channel of our Slack.
Learning Objectives This Week
Learning Objectives This Week
Be able to plot and interpret oscillatory graphs
Show mathematically how physics principles lead to oscillatory motion
Understand how damping leads to "a loss of energy" in harmonic motion
Qualitatively describe resonance phenomena
Things to think about
Things to think about
In simple harmonic motion, the position and velocity of the object are trigonometric functions in time. You know that sines and cosines are projections of points of a circle onto the x- and y-axes. What is "the circle" in simple harmonic motion?
Swings are basically simple pendulums. Maybe with damping. Based on everything in the chapter, swings shouldn't work---there's now way to ever increase the amplitude of harmonic motion. Wouldn't that violate conservation of energy? What is missing?
Homework
Homework
Quick Survey
Quick Survey
Due Wednesday.
Submission link: Quick Survey 3
Mastering Physics
Mastering Physics
Due Friday, graded for completion not for correctness. Unlimited retries. Use this to test out your understanding in a penalty-free environment. Please access Mastering Physics through the Pearson portal.
Explainer Videos
Explainer Videos
Due next Monday. This week you will have two videos; the assignments are below.
Submission link: Week 3 Explainers
Peer Review
Peer Review
To be assigned Wednesday, due next Monday.
Submission link: Week 3 peer review of Week 2 Explainers (please submit 4 times, one for each peer review)
Peer Review Assignments; if a video is missing, please email the reviewee directly. They need to (1) email you the link to their video and (2) submit using the week 2 submission form. (Note: submitting via the form won't update the peer review assignments.)
Extra Credit
Extra Credit
Apply for a summer research experience for undergraduates (REU). I strongly suggest applying off campus.
Submission link: Extra Credit (click "week 3" on drop down menu)
Explainer Video Assignments
Explainer Video Assignments
This week we'll continue to assign videos by section.
DIS (Sec 003): W 12:00 - 12:50pm
DIS (Sec 003): W 12:00 - 12:50pm
DIS (Sec 005): W: 5:00 - 5:50pm
DIS (Sec 005): W: 5:00 - 5:50pm
DIS (Sec 006): F: 8:00 - 8:50am
DIS (Sec 006): F: 8:00 - 8:50am
Hint: review the definition of the Young's modulus from the end of Ch. 14. In your video, you may want to briefly remind your reviewer what a Young's modulus means.
DIS (Sec 008): F: 10:00 - 10:50am
DIS (Sec 008): F: 10:00 - 10:50am
15.X (not in the book): "Phase space" of a harmonic oscillator.
a) Sketch the trajectory of a simple harmonic oscillator over the course of one period on the "phase space" plane. The y-axis is the velocity, rescaled by the square root of half of the mass. The x-axis is the position, rescaled by the square root of half of the spring constant. Explain the trajectory on subsequent periods.
b) Sketch the trajectory on the same plane for a damped harmonic oscillator over the course of multiple periods. For your video, sketch out the trajectory and explain the physics of what's happening. What's the significance when the trajectory crosses the horizontal axis? What's the significance when the trajectory crosses the vertical axis? Does the trajectory ever overlap itself? What does that mean?
"Phase space" plane for Problem 15.X.
The vertical and horizontal axes are normalized with a weird prefactor. That is intentional... and perhaps a hint.
For your video, please redraw these axes and sketch out the trajectory of a harmonic oscillator. This means at each point in the oscillator's motion, you need to determine the position (x-axis, up to rescaling) and the velocity (y-axis, up to rescaling).
If you go around saying "phase space" over and over again, people will think you're a graduate student in physics.
The vertical and horizontal axes are normalized with a weird prefactor. That is intentional... and perhaps a hint.
For your video, please redraw these axes and sketch out the trajectory of a harmonic oscillator. This means at each point in the oscillator's motion, you need to determine the position (x-axis, up to rescaling) and the velocity (y-axis, up to rescaling).
If you go around saying "phase space" over and over again, people will think you're a graduate student in physics.
Neat Links
Neat Links
"Comparing Simple Harmonic Motion to Circular Motion", Flipping Physics
Singing Glasses, by Science Buddies on Scientific American, Nov 16, 2015
Exploratorium: The Resonator
"Tacoma Bridge Collapse: The Wobbliest Bridge in the World?" (1940) | British Pathé
"How Swings Work," Sixty Symbols
"Swinging Physics," A Moment of Science (PBS)
Videos from Previous Offerings
Videos from Previous Offerings
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