Damped shm successive amplitude ratio

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SUMMARY

The discussion centers on the relationship between damped and undamped frequencies in simple harmonic motion (SHM). Given a damped frequency (f) of 100 Hz and a successive amplitude ratio of one half, the undamped frequency (W) can be derived using the equation w = (W^2 - c^2)^1/2, where c represents the damping factor. The key insight is that while the damped frequency remains constant, the amplitude decreases over time, leading to confusion regarding the nature of the frequencies involved.

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  • Understanding of simple harmonic motion (SHM)
  • Familiarity with damped and undamped frequencies
  • Knowledge of the damping factor in oscillatory systems
  • Basic proficiency in algebraic manipulation of equations
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Question: The damped frequency (f) is 100 Hz. The ratio of the amplitude of two successive maxima is one half. What is the undamped frequency?

My first problem is I don't understand the basic equations I'm working with. If W is the undamped angular frequency and w is the damped frequency, I was told that w = (W^2 - c^2)^1/2 where c is the damping factor. I have a problem with this however because the right side of the equation is a constant (W and c are obviously both constant) and yet the damped frequency w is constantly decreasing in a damped SHM. What's going on here?
 
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The frequency of the damped oscillator is constant. What is decreasing is the amplitude.

To answer your problem: What is the relation between the amplitude of successive maxima in terms of the frequency and the damping? How can you use this information to find the frequency if you removed the damping (i.e., how do you get W)?
 

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