Damped Oscillation: Finding Time Constant

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SUMMARY

The discussion focuses on calculating the time constant of a damped oscillator, where the amplitude decreases to 36.8% of its initial value in 10.0 seconds. The relevant equations include the exponential decay formula A(t) = A(0)e^(-kt) and the relationship between the time constant and damping coefficient, defined as time constant = m/b. A common misconception is that the decay constant k is equivalent to the time constant, which is incorrect. The correct approach involves solving for k using the given amplitude reduction and then relating it to the time constant.

PREREQUISITES
  • Understanding of damped oscillation principles
  • Familiarity with exponential decay equations
  • Knowledge of the relationship between mass (m) and damping coefficient (b)
  • Basic algebra for solving equations
NEXT STEPS
  • Study the derivation of the exponential decay formula A(t) = A(0)e^(-kt)
  • Learn how to calculate the time constant from damping ratios in oscillatory systems
  • Explore the physical significance of the time constant in mechanical systems
  • Investigate applications of damped oscillation in engineering and physics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking to clarify concepts related to damped oscillations and time constants.

Wanderer00
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Homework Statement


The amplitude of an oscillator decreases to 36.8% of its initial value in 10.0 s. What is the value of the time constant?


Homework Equations


xmax=Ae^-bt/2m
Time constant= m/b
xmax(t)= Ae^-t/2(timeconstant)


The Attempt at a Solution


I'm not quite sure where to start with this... because the intitial value isn't known so how would I even get the amplitude?

I found a solution that used A(t)=A(0)e^(-kt) and did this: 0.368A(0)=A(0)e^(-10k) and solved for k, however that wasn't right and I'm wondering why they even thought to use that equation.. is it right?
 
Last edited:
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The equation is right. But k is not the time constant if it is defined as m/b.

ehild
 

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