Week 8 notes of Physics 3LB lab at University of California, Irvine. Notes are based on the course's lab manual and are intended to help you understand the theory of "Simple Harmonic Motions in Springs."
Wk 8: Simple Harmonic Motions in Springs
Friday, February 21, 2020 4:33 PM
• Motion of a spring: F = -kx.
○ Motion w/ no friction: x = Acos(wt)
○ A = amplitude
○ w = 2pf(freq), 2pi/T, or (k/m)^1/2
○ 𝑥 = 𝑥0cos(2𝜋𝑡/𝑇)
• Eqn of motion w/ no friction: 𝑚𝑑2𝑥/𝑑𝑡2 + 𝑘𝑥 = 0
• Fig. 8.1: Measuring x, v, and a in simple harmonic motion.
○ Figure depicts a car connected to springs sliding over an air track (there is no friction).
○ Once compressed air allows car to go… The sonar ranger emits sound waves. -->
Bounces off the rectangular card on car. --> The pulse reflected back informs the sonar of
where the car is at a certain time ("Time of Arrival"). --> Converts time to voltage for
transmission to PC(personal computer).
○ PC digitizes the voltage. Uses the car's known speed to convert voltage into
position(abbreviated as x) as a function of time (this will be the VELOCITY!) Also calculates
acceleration.
○ Spring exerts a force proportional to the car's displacement --> This is simple harmonic
motion!
• The spring constant(abbreviated as k) will be studied in two springs: in series or in parallel.
• Simple Harmonic Motion: the oscillatory motion of a force that is proportional to the amount of
displacement from an equilibrium position.
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