Damped Oscillator and amplitude

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SUMMARY

The discussion focuses on calculating the time it takes for the amplitude of a damped oscillator to reduce to half its initial value. The parameters provided include a mass of 365g, a spring constant of 112N/m, and a damping coefficient of 0.117kg/s. The relevant equations used are ω=√(ω_o^2-(b/2m)^2) and ω_o=√(k/m), leading to an angular frequency (ω) of 17.5 rad/s. Participants seek guidance on progressing from this point to find the time for amplitude decay.

PREREQUISITES
  • Understanding of damped harmonic motion
  • Familiarity with the equations of motion for oscillators
  • Knowledge of angular frequency calculations
  • Basic algebra for solving exponential decay equations
NEXT STEPS
  • Calculate the time constant for the damped oscillator using the formula for amplitude decay
  • Explore the derivation of the amplitude decay formula A(t) = A_0 * e^(-bt/(2m))
  • Investigate the effects of varying the damping coefficient on the oscillation period
  • Learn about the energy dissipation in damped oscillators
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for examples of damped oscillators in practical applications.

JohnnyCollins
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1. Homework Statement [/b]
Consider the damped oscillator illustrated in the figure below. Assume that the mass is 365g, the spring constant is 112N/m, and b = 0.117kg/s. How long does it take for the amplitude to drop to half its initial value? (A*e-b*t/(2m))


http://loncapa.physics.mun.ca/res/mun/PHYSICS/serway-calc/Graphics/Graph13/serb1370.gif


Homework Equations


ω=√ω_o^2-(b/2m)^2
ω_o=√k/m

The Attempt at a Solution



I solved for ω using the two of the above equations and got 17.5 rad/s
i just don't know where to go from here, any suggestions ?
 
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