What Is the Maximum Amplitude for SHM Without Slipping?

AI Thread Summary
To determine the maximum amplitude of simple harmonic motion (SHM) for a block on a shake table without slipping, the key factors are the frequency of the motion and the coefficient of static friction. The block's acceleration can be calculated using the formula a(t) = -w^2x(t), where w is the angular frequency derived from the given frequency of 1.3 Hz. The maximum static friction force must equal the force required to keep the block from slipping, which can be analyzed using Newton's second law. The discussion emphasizes finding the maximum static friction value and the corresponding acceleration to establish the amplitude limit. Understanding these relationships is crucial for solving the problem effectively.
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Homework Statement


A block is on a horizontal surface (a shake table) that is moving back and forth horizontally with simple harmonic motion of frequency 1.3 Hz. The coefficient of static friction between block and surface is 0.59. How great can the amplitude of the SHM be if the block is not to slip along the surface?


Homework Equations


a(t)=-w^2x(t)
w=2pi*frequency


The Attempt at a Solution


I know that the accelerations of the block and the table are goin to be equal because the only horizontal force causing the block's movement is the force of static friction. But i don't know how to set up the problem. any help?
 
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could some one give me a direction? am I going in the right direction? i don't want the answer, just some help.
 
Hint: What's the maximum value of static friction between the surfaces? What acceleration does that correspond to? (Apply Newton's 2nd law to the block.)
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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