- z / τ

to the complex equation:

\overset{z}{˙} = (i A - τ^{- 1}) z + i \sum_{k} ν_{k} e^{i (g_{k} t + β_{k})} .

(1)

Its solution is

z (t) = C e^{(i A - 1/ τ) t} + k = 1 \sum 2 \frac{ν _{k}}{g _{k} - A - i / τ} e^{i (g_{k} t + β_{k})} .

(2)

Unlike the undamped free eccentricity, the homogeneous term decays exponentially. The forced response survives, acquires a phase lag, and has finite amplitude

\frac{∣ ν _{k} ∣}{( g _{k} - A ) ^{2} + τ ^{- 2}} .

(3)

 Ancestors (10)

3
Paper 316
iii
2025
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
List of universities
 Home

 View article source

 Discussion (0)

New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 316 / 3 / v

Solution

 Ancestors (10)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 316 / 3 / v

Solution

 Ancestors (10)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)