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.
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.
