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physics help oscillation question? | Yahoo Answers

source : yahoo.com

physics help oscillation question? | Yahoo Answers

The reason that no one has answered this question to date is that we don’t know the dampening effect of air. Does it vary with v^2 (high speed drag) or v (low speed drag)?

I will make an assumption that it varies with velocity. What this means is that the decay will be just like your half-life equations.

let a = amplitude

da/dt = -λ a

da/a = -λ dt

∫ 1/a da = ∫ -λ dt

ln a = -λ t + c

a(t) = e^c *e^-λ t

a(0) = a.i = 100% = 1

a(0)= 1 = e^c *e^(-λ*0)

1 = e^c * 1

e^c = 1

c = 0

a(50s) = .6

.6 = e^(-λ *50s)

ln 0.6 = -λ * 50s

λ = -(ln0.6 )/50s

λ = 0.010217

===> a(t) = e^(-0.010217 t)

a(t) = .3

.3 = e^(-0.010217 t)

ln .3 = -0.010217 t

====> t = 117.8 s

**************

If you don’t know calculus, you probably solve it like this:

a = a.i * e^-λ t …. http://www.wolframalpha.com/input/?i=exponential+d…

where a.i = initial amplitude

a/a.i = e^-λt

λ = ln 0.6 / 50s

for a = .3 a.i

t = 117.8s

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