- #1

SteveDB

- 17

- 0

hi all.

Some clarification on this would be helpful to get me going in the correct direction.

For a specified system, I'm trying to prove that the time it takes for the system to decay to 1/e of its original value (which works out to ~36.8%), takes a certain amount of time. The actual values are unimportant but the process is.

I have gone through my classical mech book-- 4th ed of Marion Thornton, as well as my diff/eq book-- 5th ed of Nagle, Saff, Snider, and of course my waves and oscillation text-- A.P.French, and cannot decipher what seems-- or I thought would be-- a fairly straightforward problem.

I'm not schooled/skilled in latex, so please bear with my "hand version."

I've taken the time derivative of the energy, and get a m/s^3 function for my acceleration value. With the values for b, k, and m, I do not get the time I'm looking to prove.

m*x_dbldot + b*x_dot + k*x = 0

Where x(t) = (A*exp(omega*t) +B*exp(-omega*t)

The rate given for decay to 1/e is:

E/delta_E

Where delta_E is given by -b*E/(m*nu)

where nu is given by omega_o/2pi.

I've also tried the quality value Q for this. I know I'm missing something, but can't quite identify it.

A detailed explanation of this would be deeply appreciated.

Best regards,

Thank you.

Some clarification on this would be helpful to get me going in the correct direction.

For a specified system, I'm trying to prove that the time it takes for the system to decay to 1/e of its original value (which works out to ~36.8%), takes a certain amount of time. The actual values are unimportant but the process is.

I have gone through my classical mech book-- 4th ed of Marion Thornton, as well as my diff/eq book-- 5th ed of Nagle, Saff, Snider, and of course my waves and oscillation text-- A.P.French, and cannot decipher what seems-- or I thought would be-- a fairly straightforward problem.

I'm not schooled/skilled in latex, so please bear with my "hand version."

I've taken the time derivative of the energy, and get a m/s^3 function for my acceleration value. With the values for b, k, and m, I do not get the time I'm looking to prove.

m*x_dbldot + b*x_dot + k*x = 0

Where x(t) = (A*exp(omega*t) +B*exp(-omega*t)

The rate given for decay to 1/e is:

E/delta_E

Where delta_E is given by -b*E/(m*nu)

where nu is given by omega_o/2pi.

I've also tried the quality value Q for this. I know I'm missing something, but can't quite identify it.

A detailed explanation of this would be deeply appreciated.

Best regards,

Thank you.

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