# Lets narrow it to two cases case 1 your voltage data

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the selection over the data. Let’s narrow it to two cases: Case 1: Your voltage data grows before peaking and then decaying to zero. Case 2: Your data looks simply like an exponential decay. Either way, use the following set of equations: V ( t ) = V 0 e - t / 2 τ sinh ωt τ = L R ω = r R 2 4 L 2 - 1 LC >> modelOver = @ ( p , x ) p (1) . exp ( - x ./(2 p (2) ) ) . sinh ( p (3) . x + p (4) ) + p (5) ; p(1): V 0 ; in case 1 you can probably just guess the value of the peak. Case 2: use your initial voltage point. p(2): τ , and p(3): ω ; these are confusing to interpret for most people, the safest thing is to use your predicted values from the equations above. p(4): This is the phase φ . In case 1, φ 0 so start there and slowly increase it until it fits. For case 2, φ π/ 2. p(5): A vertical shift in the data that is approximately zero. 4 Frequency Domain Amplitudes For the frequency domain, we are modelling the following equation: | V ( ω ) | = V 0 R/R t r 1 + Q 2 ω ω 0 - ω 0 ω 2 2

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Also, be aware that these are angular frequencies, so you’ll need to convert your linear frequen- cies (in Hz) by ω = 2 πf . >> x = 2 pi x ; % convert your f r e q . to angular f r e q . , only i f you haven t already >> modelFrequency = @ ( p , x ) p (1) . / s q rt (1+ p (2) ˆ2. ( x . / p (3) - p (3) . / x ) . ˆ 2 ) | V ( ω 0 ) | = V 0 R/R t , so find the peak in your data; its y-value is p(1) and its x-value is p(3).
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