Calculating amplitude after 50 oscillations

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SUMMARY

The discussion focuses on calculating the amplitude of an oscillator after 50 oscillations, given an initial amplitude of 6.40 cm and a decay rate of 2.50% per oscillation. The user struggles with the formula for amplitude decay and seeks clarification on the relationship between the initial amplitude and the amplitude after multiple oscillations. The correct approach involves using the formula A = Ai * k^n, where k represents the remaining amplitude percentage after each oscillation, and n is the number of oscillations.

PREREQUISITES
  • Understanding of oscillatory motion and amplitude decay
  • Familiarity with exponential decay formulas
  • Basic algebra for manipulating equations
  • Knowledge of the concept of percentage decrease
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  • Research the formula for exponential decay in oscillatory systems
  • Learn how to derive the general formula for amplitude after multiple oscillations
  • Study the impact of damping on oscillatory motion
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Students studying physics, particularly those focusing on oscillatory motion and exponential decay, as well as educators looking for examples of amplitude calculations in real-world scenarios.

marshall104
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Homework Statement



An oscillator with a mass of 600 g and a period of 1.20 s has an amplitude that decreases by 2.50% during each complete oscillation. If the initial amplitude is 6.40 cm, what will be the amplitude after 50.0 oscillations?


Homework Equations



How do I approach this problem. I am so confused

Ive been using xmax=Ae(-t/2x)

with no luck. any help would be great



The Attempt at a Solution



m=600g
T=1.2s
amplitude decreases by 2.5%
I think my problem is I don't understand were xmax is coming from or even how to find it. A hint is great!

Thanks.
 
Physics news on Phys.org


After one oscillation, what percentage of the initial amplitude will the actual amplitude be? Call this percentage k. After one oscillation, A=kAi. After two, A=k*k*Ai. After 5, A=k*k*k*k*k*Ai. What's the general formula for A in terms of Ai?
 

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