What Is the Maximum Amplitude for SHM Without Slipping?

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SUMMARY

The maximum amplitude of simple harmonic motion (SHM) for a block on a shake table without slipping is determined by the static friction coefficient and the frequency of motion. Given a frequency of 1.3 Hz and a static friction coefficient of 0.59, the maximum acceleration can be calculated using the formula \( a(t) = -w^2x(t) \), where \( w = 2\pi \times 1.3 \). The block will not slip as long as the acceleration does not exceed the maximum static friction force divided by the block's mass, which can be derived from Newton's second law.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Knowledge of static friction and its coefficient
  • Familiarity with Newton's second law of motion
  • Ability to calculate angular frequency from frequency
NEXT STEPS
  • Calculate the maximum static friction force using the coefficient of static friction.
  • Learn how to derive acceleration from angular frequency in SHM.
  • Explore the relationship between force, mass, and acceleration in Newton's second law.
  • Investigate the implications of varying frequency on the amplitude of SHM.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators looking for examples of static friction in motion scenarios.

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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.)
 

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