The discussion revolves around solving the equation involving complex numbers and exponential decay, specifically the equation $$\cos(\omega t) = 1 - e^{-(\frac{t}{RC})$$ where the goal is to solve for the variable t while treating R, C, and ω as constants.
The discussion is ongoing, with participants exploring various interpretations of the problem. Some guidance has been offered regarding the potential need for numerical solutions if specific values for the constants are known, while others express skepticism about the existence of a closed-form solution.
There is an acknowledgment of the need for numerical values for R, C, and ω to proceed with a solution, indicating that the problem may not be solvable in a general form without additional information.
If you know values for ##R,~C,~\omega## you can solve it numerically. Otherwise you are out of luck.iScience said:Homework Statement
goal: solve for t; all else are constants
$$cos(\omega t)=1-e^{-(\frac{t}{RC})}$$
iScience said:Homework Statement
goal: solve for t; all else are constants
$$cos(\omega t)=1-e^{-(\frac{t}{RC})}$$Homework Equations
noneThe Attempt at a Solution
i turned the cos to complex notation & rearranged
$$e^{i\omega t}+e^{-(\frac{t}{RC})}=1$$
$$ln(e^{i\omega t}+e^{-(\frac{t}{RC})})=0$$
and i am stuck..