Harmonic motion and the coeffcieient of friction

AI Thread Summary
The discussion focuses on calculating the coefficient of static friction between a tray and a cup during simple harmonic motion. The tray oscillates at a frequency of 2.00 Hz with an amplitude of 0.05 m, causing the cup to slip. Participants discuss deriving the maximum velocity and the necessary acceleration to maintain static friction, emphasizing the relationship between acceleration, gravitational force, and the coefficient of friction. The equation a = -kx/m is highlighted, where k/m can be determined from the period of motion. Understanding these dynamics is crucial for accurately calculating the coefficient of static friction.
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1. A tray is moved horizontally back and forth in simple harmonic motion at a frequency of f=2.00Hz. on this tray is an empty cup. obtain the coefficient of static friction between the tray ad cup given that the cup begins slipping when the amplitude of the motion is 0.05m

2. f=kx
angular frequency=2(pi)f



3. i managed to solve for the max velocity and got an answer of 0.628 but i am not sure how to correlate that to the coefficient of static friction. I think i have done it correctly so far. If not can somebody please guide me or lead me to the next step.


thnx
ty
 
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how did you get max velocity? The problem is about what acceleration is needed to achieve a condition where ma>mg(mu).
so a>g*mu. So you need "a" as a functon of displacement, which is simply
-kx/m. The quantity k/m can be determined from the period.
 

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