Revised Harmonic Ocillator, Period and Why gravity doesn't matter

The Harmonic oscillator period is proportional to the square root of the mass, because the acceleration is inversely proportional to the mass, and period is proportional to 1/the square root of the acceleration. This is just as true in vertical and as in horzontal oscillators.

The period's relationship to the mass has nothing to do with the spring having to overcome greater gravitational force. The gravitational force is "automatically" canceled by the spring being stretched to its NEW EQUILBRIUM position. In other words the force the spring exerts on the mass while in the new equilibrium position already is equal to mg upward. Thus , if we add this +mg from the spring into our equations and also add the -mg due to the force of gravity, they cancel and we are left with exactly the same equations about the new equlibrium position that we would have for a horizontal spring/mass about the original relaxed (equilbrium) position of the spring. See me if this not yet clear to you.

Harmonic Oscillator Vmax is proportional to A not sqrt A

In your ocillator lab reports, a large number of you are telling me that Vmax is proportional to A^1/2, despite the fact that your graphs clearly show Vmax is linear with A, NOT with the square root of A. In fact your graphs all show that Vmax =omega x A. All of which makes the fact that you answer the question saying Vmax is propoertional to A^1/2 a complete mystery to me. From where are you getting this misinformation? In any case, please correct your reports.

A, of course is amplitude, which is the maximum displacemnt from the equilbrium.

Solutions to Some AP Chapt 15 Porblems

Here is a slightly readable PDF.

I haven't checked the arithmetic carefully but the approach is what's important.

APChapt15Solns07.PDF

Solutions to Electrostatics Worksheet 2

The moment you've been waiting for! Well maybe not, but here are the solutions for AP Unit 10 WS2


SolnsElectrostaticsWS2.doc

AP Wave Retest Info

AP students who had a raw score below 82 on the last wave test are eligible for a retest on Wednesday outside of class hours, provided they attend a mandatory review session either Tuesday after school or Wednesday at 7AM. The maximum grade you will be credited with will be the equivalent of an 82 (strong B-). You must also bring in corrections to the original test to qualify.

Note on Standing Wave Nodes

Many of you working on the standing wave lab confused the condition for an antinode and odd half periods with the conditions for a node. Note that there is usually no difference in effect between odd and even WHOLE periods. Odd HALF periods are needed for ANTInodes if a phase shift occurs on reflection. [SEE the Notes published on Feb 12 on this blog]

For a point on a string or similar medium to be a standing wave node, waves arriving from the left and from the right must be out of phase at all times. A fixed end produces a half cycle wave shift in a reflected wave. If a wave passes through a node say going left travels to a fixed end and gets reflected by the fixed end and then travels back that is to the right ( now shifted by half a cycle) to that node, it will arrive at the node out of phase with waves traveling to the left if it takes ANY INTEGER (even or odd) number of periods to make the round trip from node to end and back to node.

This is consistent with the fact that there are an integer number of loops between any node and any fixed end and each loop is half a wavelength. Therefore the round trip will include twice the number of loops as the one way trip from node to the end and therefore an even number of loops. The number of loops is equal to half as many wavelengths but half of an even number is always an integer. Therefore the round trip is an integer number of wavelengths and takes an integer number of periods. [ Remember wavelength = speed x period so a distance of N wavelengths takes a time of N periods].

AP Free Response Package

As you know, your free response package is due Monday. In order to facillitate reviewing the material, please prepare your solutions on separate clean sheets as requested in the instructions you received. Then, transfer the key parts of your solution to the problem sheets. This way we can go over the problems even though you have submitted your assignment on the separate sheets. The district's email system seems to be having a nervous breakdown, but you can reach me by submitting comments to this blog.

Enjoy the rest of your break.

Dr. Cherdack

Honors Break Assignment, Retest Data

Here are two worksheets for your assignment over the break. They are due Monday. You must make a serious attempt to meet with your new group at least once. Each student must write a paragraph about what you did at the meeting. I hope it includes some work on physics. The Unit Number on these is 10 not the Unit 9 we are currently on because they are from my AP class.

Also, for those who got a raw score of 67 or less on the wave test, you can take a retest on Tuesday, provided you come to a mandatory study session Monday after school or Tuesday before school by 7 AM. If you do not know your score you can email me.

Unit10Worksheet1.doc

Unit10Worksheet2.doc

AP Assignment due Fri 2/16

AP, as promised, here is your assignment for tomorrow Friday 2/16

Unit10Worksheet2.doc

Extra Credit Wave Problem

As promised, here is an extra credit porblem on waves. Its tough, but it will provide another perspective on waves as traveling oscillations. It will also give you some glimmer of differential calculus.

ExtraCreditProblemonW.doc

Simple Harmonic Motion Lab Sample

I have posted a sample of the Simple Harmonic Motion Lab. Please refer to this to for correcting your lab report since it will show you what was expected. This is much more efficient than writing the same comments a few dozen times. Note that I used a stronger spring and some different masses to get my data, so use this sample as a guide and don't expect your results to match it numerically.

SampleSimpleHarmMotLab.doc

Corrected Solutions for Homework

You can use this link to the corrected solutions. In addition to problem 5 I have corrected the phase shifts for questions on reflection to pi from pi/2. I meant 1/2 cycle, which of course is pi NOT pi/2.

HmwrkonOscillsWavessolns.doc

Correction 2

It was Molly Kirk who found and reported the error to my solution to problem 5. My apologies to her.

Notes on Standing Waves

Do NOT confuse crests or troughs with nodes. Maximum crests and minimum troughs have the same amplitude, just different signs, and occur at antinodes. Nodes ( not antinodes) are where there is no change because there is always destructive interference. A wave crest passing through a point going to the left will come back reflected from a fixed end as a trough going to the right. If the point is to be an antinode this reflected wave must return to the point an odd number of half periods later so that another, unreflected (i.e.”original”) wave going to the left will also be a trough, so that you will have constructive interference between the two waves.

For a place to be a node other than at the end of the string, it must have continuous destructive interference. That means that the wave reflected with a phase change must arrive an integer number of periods after the original wave passes through, or 2 x distance from node to end = integer number of wavelengths. The distance between a node and any antinode is always an odd number of quarter wavelengths. The distance between any two nodes is an integer number of half wavelengths. The distance between two antinodes is an integer number of half wavelengths. Draw a sketch and you will see all this.

New Corrections to Lab and Homework Prob 5

Standing Wave Lab has error pointed out by Laura Goldberg. The relationship is between lambda and sqrt of [FT/(M/L)] NOT square of [FT/(M/L)].

Molly Hahn dropped me a note about correcting the solution to number 5 . She pointed out that the square root of (6.4 E10/2.5E3) is 5059 m/s and this is the correct answer for the wave speed. Therefore the correct answer for the wavelength is 10.2 m and for the wave speed in the second material is 7133 m/s. Sorry, I calculated the orignal speed for Y =6.4E11 N/m^2 for some unknown reason.

Solutions to Oscillator and Wave Homework

Here are preliminary solutions to the assignment posted Saturday. I haven't checked them yet so be careful. Try to do the assignemnts without seeing the solutions first. For AP students, only those you solve on your own count for extra credit. Your on your honor.

HmwrkonOscillsWavessolns.doc

Oscillator Wave Homework

Here is the mandatory assignment for Monday for Honors. It wouldn't hurt AP students who have time to look at them. In fact for AP I'll make it 5 points of extra credit for each problem you do, but only if you have completed your required homework to date.

HmwrkonOscillsandWaves.doc

I will try to post solutions for about half of this by Sunday 6 PM I may get to it sooner. Try your best and think about waves as trvelling oscillations that do carry energy and even momentum.

Enjoy yourweekend.

Links to Wave Speeds

Here are links to wave speeds

NotesonTransverseWaveSpeedR1.doc

MaterialPropertiesandLongr1.doc

Extra Credit

Anyone handing a slip of paper with hisor her name on it and saying "I read the blog last night" on Wednesday will get 5 points of extra credit.

Revised Schedules for Honors AND AP

Here are revised schedules

Honors Unit 8
HonUnit8harmschedR1only07.doc

AP Unit 9

APUnit9harmschedonlyR107.doc

Science Programs

Rutgers runs an astrophysics program during the summer with follow on real research programs in the fall. Columbia University runs a Saturday science program which has had good participation from Ridge students recently.

Try their web sites for more info. If that doesn't work, come see me.

Biomedical Research Opportunity for Juniors

Here's an opportunity some of you may be interested in. Sounds more legal and philosophical than scientific, but that's probably just the way it was written up. There probably will be some real science content.

For two weeks in July, twelve former juniors (i.e. current 11th graders) will be selected to experience research up close at several of the Garden State's prestigious institutions during NJABR's third High School Summer Biomedical Research Fellowship Program.

From July 9 through July 20, students will visit a different New Jersey research facility each day. They will learn about the laws and regulations in place to protect both human and animal subjects and address ethical issues arising from the rapid advance of science and technology.
Note: This is not a residential program. Each day, Fellows assemble at a central location and travel by bus to meet with and learn from dedicated scientists engaged in different aspects of the discovery process, who share career information along with insight into their piece of the research process. The Program exposes the Fellows to the essence -- and essential components -- of biomedical research. The experience includes hands-on science, lectures, demonstrations and tours with time for one-on-one discussions with inspiring role models.

The Fellowship Program is open only to current high school juniors interested in medicine and the Life Sciences.

A full description of the 2006 Summer Program can found on NJABR's website: www.njabr.org.

2007 applications are also available on NJABR's website: www.njabr.org.

The deadline for completed applications is March 30, 2007.

For more information, call 908/964-9449.




New Jersey Association for Biomedical Research (NJABR) is a not-for-profit coalition of the state's leading research institutions, health voluntaries and allied groups dedicated to improving human and animal health.

Corrections to Review Problems Rotational Dynamics, Harmonic Motion, and Waves

Several students in my Honors Physics class complained that in two cases of problem 6 I had created problems that reflected inappropriate situations, i.e the maximum angles of displacement for the pendulum did not make much sense for the 3 and 4 kg cases. They are correct. For the 3 kg case its a bit too large for accuracy; for the 4kg case it is too large for pendulum motion at all.

I would like to point out that the only reason they had difficulties with this problem is because of their defective eyesight. Apparently these poor students have trouble seeing the decimal points in numbers just because I neglected to put them in. A pretty lame excuse if you ask me.

The difficulties for the 3 kg case arise from the energy being 50 J instead of the 5.0 J it should have been. This results in a maximum displacement angle of 1.05 radians. While this is physically okay ( its about 60 degrees from vertical), it violates the small angle approximation that allowed us to say phi = sin phi in deriving the equation for omega for a pedulum. Thus the equation we used is not valid for the situation we analyze here.

The 4 kg case is even worse, since the 15m/s ( it should have been 1.5 m/s) vmax yields a maximum angle of 2.5 radians. While at 143 degrees from straight down, this is still less than straight up, with an angle like this all bets are off since the mass would tend to fall straight down rather than describe an arc the way all well bred pendulums do.

In any case, I am going to post the sheet with a revised table for Problem 6 for these nitpickers who insist on reading numbers as I typed them instead of as I should have typed them. The corrections are use 5J for the 3 kg case and 1.5 m/s for the 4 kg case. Just to show there are no hard feelings I will even post the solutions to the corrected problem.

Here is the revised problem sheet with just the changes I mentioned:

RevProbRotandHarmR2.doc

and here are the solutions for the corrected problems. SolnsforRevProbRotHarWaves.xls

Again, the difference is that energies ,velocities, and the phi max are now more reasonable for the 3 and 4 kg cases for problem 6.

Wave Speed

I have an unreasonably large number of leftover wavespeed sheets, both longitudinal and transverse. Make sure you have picked yours up. AND READ THEM!!!

Great Lecture on Black Holes

What I expect will be an outstanding lecture on black holes will be given at Rutgers on March 3 at 2 PM. The lectures are aimed at a popular audince and the speaker is usually chosen for both his outstanding expertise and his ability to communicate to the non-expert. You can get more info at:

www.physics.rutgers.edu/colloq/irons/

or come see me.