PAGE EDITORS: Bradley Jackson, Carlos Barrera, Tijana Canic, and Alfredo Cubina

Natland Note: (12/10/13)

  • make sure that each of you are posting things
  • post sample problems that some have already posted on facebook/taken pictures of (or come by to get some)
  • remember pictures, links, and the self-made video (who is going to do this?)
  • make sure the notes don't get cut off!
  • list the sample questions that we did in class (text and ranking) >>Look at the forces wiki for formatting here.
  • post rest of the notes
  • remember to list the SOURCES for everything you post on the bottom of the wiki.

Wiki is due, Completed, on Monday (review day).

NOTES:

Simple Harmonic Motion1.jpeg

Simple Harmonic Motion1 1.jpeg

notes 1.jpg



RELEVANT DIAGRAMS!


As in the formula T=2*pi*sqrt(m/k), a more massive object oscillating has a longer period.
physics2.gif





An object in simple harmonic motion reaches maximum velocity when a spring's x=0, and reaches maximum acceleration when x=A (amplitude).
physics.gif

This picture illustrates how kinetic and potential energy change throughout the period

energy.gif


Hey Mr. Natland, I made a video but the file size is too large for the wiki. Any suggestions?
-Bradley


Awesome video by a professor at MIT


Video solving a simple harmonic motion problem:

http://www.youtube.com/watch?v=yNVWIb6jChY

An acoustician looking at the relationship between music, springs, and pendulums:

http://www.youtube.com/watch?v=YyOUJUOUvso

"Physicists Couple Oscillating Ions"

http://physicsworld.com/cws/article/news/2011/feb/23/physicists-couple-oscillating-ions





SAMPLE PROBLEMS:

*Keep in mind these answers may be wrong, they have not been checked yet*
19.) An object executing simple harmonic motion has a maximum speed of 4.3 m/s and a maximum acceleration of 0.65 m/s^2. Find (a.) the amplitude and (b.) period of this motion.
Answer: (a.) 28.44615385m (b.) 41.56568742s

30.) A spring with a force constant of 65 N/m is attached to a 0.50-kg mass. Assuming that the amplitude of motion is 3.1 cm, determine the following quantities for the system: (a.) w [aka omega], (b.)Vmax, and (c.) T [period]
Answer: (a.) 11.40175425 rad/s (b.) 0.3534543818 m/s (c.) 0.551071806s

31.) Two people with a combined mass of 125 kg hop into and old car with worn out shock absorbers. This causes the springs to compress by 8.oo cm. When the car gits a bump in the road it oscillates up and down with a period of 1.65 s. Find (a.) the total load supported by the springs and (b.) the mass of the car.
Answer:

32.) a O.65-kg mass attached to a vertical spring of force constant 150 N/m oscillates with a maximum speed of 0.35 m/s. Find the following quantities related to the motion of the mass: (a.) the period. (b.) the amplitude, (c.) the maximum magnitude of the acceleration.
Answer: (a.) 0.4729810071s (b.) 0.0263470428m (c.) 4.649483433 m/s^2

42.) A bunch of grapes is placed in a spring scale at a supermarket. The grapes oscillate up and down with a period of 0.45 s. and the spring in the scale has a force constant of 650 N/m. What are (a.) the mass and (b.) the weight of the grapes?
Answer: (a.) 3.334100197 kg (b.) 32.67418193N

43.) What is the maximum speed of the grapes in the previous problem, if their amplitude of oscillation is 2.3 cm?
Answer: 0.3211405825 m/s

48.) A large, simple pendulum is on display in the lobby of the United Nations building. If the pendulum is 10.0 m in length, what is the least amount of time it takes for the bob to swing from a position of maximum displacement to the equilibrium position of the pendulum? ( Assume that the acceleration of gravity is g=9.81 m/s^2 at the UN building)
Answer: 1.585934962s

49.)Find the length of a simple pendulum that has a period of 3.00s. Assume that the acceleration of gravity is g= 9.81 m/s^2
Answer: 2.236411826m

50.) If the pendulum in the previous problem was to be taken to the moon, where the acceleration of gravity is g/6, (a.) would its period increase, decrease, or stay the same? (b.) Check your results in part (a.) by calculating the period of the pendulum on the Moon.
Answer: (a.) T will be greater (b.) 7.352217491


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Answer:









WEBSITES:
http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html
Great website for calculating angular frequency, period, and displacement to understand the relationships between the variables.

http://www.physicsclassroom.com/class/waves/u10l0c.cfm
Provides a thorough analysis of the forces acting during pendulum motion















SOURCES:

http://www.richtherrn.net/physics/answershoproblems.htm
http://dev.physicslab.org/Document.aspx?doctype=3&filename=OscillatoryMotion_SHM.xml