Damped harmonic motion question

  • Thread starter aks_sky
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  • #1
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A damped harmonic motion starts from rest at time t=0 with displacement A0 has the equation:

x(t) = A0/cos (delta)*e^(-t/tau) *cos (w't + delta)

w' is the angular frequency, tau is the time constant and delta is given by:

tan (delta) = - (1/w' tau)

find the time when the maximum negative displacement occurs. express it in terms of period.



So, Can you just give me a hint on where to start and where to go from there.

Thank you
 

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  • #2
kuruman
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Hint: Which term in your expression for x(t) can conceivably turn negative as time increases? Is it the exponential or is it the cosine?
 
  • #3
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That would be the exponential since we have -t in there. So i guess in this case i am supposed to differentiate with respect to t first?
 
  • #4
kuruman
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Just wait before you take any derivatives.

[tex]e^{-t}=\frac{1}{e^t}[/tex]

For what value of t is the expression negative?
 
  • #5
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oh oops i dint see that part. The exponential is going to give me a positive value. How did i forget that. my bad
 
  • #6
kuruman
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Do you know where to go from here? The first thing to do is to find a value for the phase delta.
 
  • #7
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I dont know exactly where to go since i am confused about what it is asking for exactly. And to find the value for delta i will be using the tan (delta) = (1/w' tau) and then i guess i can substitute w' = 2*pi/ T' in there and go from there?
 
  • #8
kuruman
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You are given x(t) and you are told that at t = 0, the oscillator is at A0. If you evaluate your expression at t = 0, i.e. find x(0), is it equal to A0 or is it equal to something else?
 
  • #9
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ohhh i see.. no problemo.. thank you
 

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