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- Thread starter Jozefina Gramatikova
- Start date

In summary, the homework equation is ## A e^{-\frac{b}{2m} t}=\frac{1}{2} Ae^{-\frac{b}{2m} 0} ##, and the amplitude halves after 3.036 seconds.f

- #1

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- #2

- 5,473

- 2,790

- #3

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I don't know how much is x(t)The damping coefficient is ## b ## in your formula. Do you know how to solve ## e^{-\frac{b}{2m}t}=\frac{1}{2} ## for ## t ## ? .

- #4

- 5,473

- 2,790

The sinusoidal oscillation is assumed to happen at a much higher frequency with small damping, so that the period of the oscillation ## T ## is quite short, and you don't need to consider the term ## \cos(\omega t ) ##. The amplitude is ## A e^{- \frac{b}{2m} t} ##.I don't know how much is x(t)

- #5

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Ok, thank you and what about x(t)The sinusoidal oscillation is assumed to happen at a much higher frequency with small damping, so that the period of the oscillation ## T ## is quite short, and you don't need to consider the term ## \cos(\omega t ) ##. The amplitude is ## A e^{- \frac{b}{2m} t} ##.

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- #8

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- #9

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Yeah, I know how to proceed from here ## A e^{-\frac{b}{2m} t}=\frac{1}{2} Ae^{-\frac{b}{2m} 0} ##,. I got t=3.036s. I hope that this is correct

- #10

- 5,473

- 2,790

- #11

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That's true. I did plug 0.69. Thank you!

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