Calculus Volume 3 · 免费预览
非齐次线性方程
非齐次方程是在齐次方程的通解上再加一个特解。两种方法为待定系数法与常数变易法。当激励与某一固有频率相同时，便会产生共振。
1. The general solution's structure
The general solution's structure
2. Undetermined coefficients
Undetermined coefficients
3. Variation of parameters
Variation of parameters
4. Resonance and the forced oscillation
Resonance and the forced oscillation
5. General solution structure
The general solution of the nonhomogeneous equation is which sum?
6. Undetermined coefficients guess
For the forcing g = e^(kt), the undetermined coefficients method guesses which form?
7. Resonance signature
When the forcing's frequency matches the natural frequency, the resonance's signature in the solution is what?
8. Variation of parameters scope
The variation of parameters method handles which forcings?
9. Transient and steady state
In the forced damped oscillation, the homogeneous's decaying part and the persistent particular are called what?
10. Resonant guess multiplier
At resonance the guess gains a factor of which variable? Answer with one lowercase letter.
11. Beat frequency
Near resonance the alternating amplitude has which two-word name? Answer like answer key.
12. Wronskian denominator
The variation of parameters divides by which determinant? Answer with one word.
13. Damping's effect on resonance
Including damping, the resonant response becomes which instead of unbounded?
14. Complementary solution
The homogeneous's general solution is also called which two-word name? Answer like answer keys.