续表
页码标注：· 6 ·
| 序号 | 象函数 \(F(s)\) | 原函数 \(f(t)\) |
|---|---|---|
| 21 | \(\dfrac{s+a_0}{(s+a)^2+\omega^2}\) | \(\dfrac{1}{\omega}\left[(a_0-a)^2+\omega^2\right]^{1/2}\mathrm{e}^{-at}\sin(\omega t+\varphi)\) \(\varphi=\arctan\dfrac{\omega}{a_0-a}\) |
| 22 | \(\dfrac{s+a}{(s+a)^2+\omega^2}\) | \(\mathrm{e}^{-at}\cos\omega t\) |
| 23 | \(\dfrac{1}{s\left[(s+a)^2+\omega^2\right]}\) | \(\dfrac{1}{a^2+\omega^2}+\dfrac{1}{(a^2+\omega^2)^{1/2}\omega}\mathrm{e}^{-at}\sin(\omega t-\varphi)\) \(\varphi=\arctan\dfrac{\omega}{-a}\) |
| 24 | \(\dfrac{s+a_0}{s\left[(s+a)^2+\omega^2\right]}\) | \(\dfrac{a_0}{a^2+\omega^2}+\dfrac{\left[(a_0+a)^2+\omega^2\right]^{1/2}}{\omega(a^2+\omega^2)^{1/2}}\mathrm{e}^{-at}\sin(\omega t+\varphi)\) \(\varphi=\arctan\dfrac{\omega}{a_0-a}-\arctan\dfrac{\omega}{-a}\) |
| 25 | \(\dfrac{s^2+a_1s+a_0}{s\left[(s+a)^2+\omega^2\right]}\) | \(\dfrac{a_0}{a^2+\omega^2}+\dfrac{\left[(a^2-\omega^2-a_1a+a_0)^2+\omega^2(a_1-2a)^2\right]^{1/2}}{\omega(a^2+\omega^2)^{1/2}}\mathrm{e}^{-at}\sin(\omega t+\varphi)\) \(\varphi=\arctan\dfrac{\omega(a_1-2a)}{a^2-\omega^2-a_1a+a_0}-\arctan\dfrac{\omega}{-a}\) |
| 26 | \(\dfrac{1}{(s+c)\left[(s+a)^2+\omega^2\right]}\) | \(\dfrac{\mathrm{e}^{-ct}}{(c-a)^2+\omega^2}+\dfrac{\mathrm{e}^{-at}}{\omega\left[(c-a)^2+\omega^2\right]^{1/2}}\sin(\omega t-\varphi)\) \(\varphi=\arctan\dfrac{\omega}{c-a}\) |
| 27 | \(\dfrac{s+a_0}{(s+c)\left[(s+a)^2+\omega^2\right]}\) | \(\dfrac{a_0-c}{(a-c)^2+\omega^2}\mathrm{e}^{-ct}+\dfrac{1}{\omega}\left[\dfrac{(a_0-a)^2+\omega^2}{(c-a)^2+\omega^2}\right]^{1/2}\mathrm{e}^{-at}\sin(\omega t+\varphi)\) \(\varphi=\arctan\dfrac{\omega}{a_0-a}-\arctan\dfrac{\omega}{c-a}\) |
| 28 | \(\dfrac{1}{s(s+c)\left[(s+a)^2+\omega^2\right]}\) | \(\dfrac{1}{c(a^2+\omega^2)}-\dfrac{\mathrm{e}^{-ct}}{c\left[(a-c)^2+\omega^2\right]}+\dfrac{\mathrm{e}^{-at}}{\omega(a^2+\omega^2)^{1/2}\left[(c-a)^2+\omega^2\right]^{1/2}}\sin(\omega t-\varphi)\) \(\varphi=\arctan\dfrac{\omega}{-a}+\arctan\dfrac{\omega}{c-a}\) |
| 29 | \(\dfrac{s+a_0}{s(s+c)\left[(s+a)^2+\omega^2\right]}\) | \(\dfrac{a_0}{c(a^2+\omega^2)}+\dfrac{(c-a_0)\mathrm{e}^{-ct}}{c\left[(a-c)^2+\omega^2\right]}+\dfrac{\mathrm{e}^{-at}}{\omega(a^2+\omega^2)^{1/2}}\left[\dfrac{(a_0-a)^2+\omega^2}{(c-a)^2+\omega^2}\right]^{1/2}\sin(\omega t-\varphi)\) \(\varphi=\arctan\dfrac{\omega}{a_0-a}-\arctan\dfrac{\omega}{c-a}-\arctan\dfrac{\omega}{-a}\) |
| 30 | \(\dfrac{1}{s^2(s+a)}\) | \(\dfrac{\mathrm{e}^{-at}+at-1}{a^2}\) |
| 31 | \(\dfrac{s+a_0}{s^2(s+a)}\) | \(\dfrac{a_0-a}{a^2}\mathrm{e}^{-at}+\dfrac{a_0}{a}t+\dfrac{a-a_0}{a^2}\) |
| 32 | \(\dfrac{s^2+a_1s+a_0}{s^2(s+a)}\) | \(\dfrac{a^2-a_1a+a_0}{a^2}\mathrm{e}^{-at}+\dfrac{a_0}{a}t+\dfrac{a_1a-a_0}{a^2}\) |
| 33 | \(\dfrac{s+a_0}{(s+a)^2}\) | \(\left[(a_0-a)t+1\right]\mathrm{e}^{-at}\) |
| 34 | \(\dfrac{1}{(s+a)^n}\) | \(\dfrac{1}{(n-1)!}t^{n-1}\mathrm{e}^{-at}\) |
| 35 | \(\dfrac{1}{s(s+a)^2}\) | \(\dfrac{1-(1+at)\mathrm{e}^{-at}}{a^2}\) |
| 36 | \(\dfrac{s+a_0}{s(s+a)^2}\) | \(\dfrac{a_0}{a^2}+\left(\dfrac{a-a_0}{a}t-\dfrac{a_0}{a^2}\right)\mathrm{e}^{-at}\) |