求下列函数的 Laplace 逆变换[br][/br][tex=4.143x2.429]iw827m0GuJXkG33qVP/q5Z3Hwmo8zBcFTgZMLwcLBnQ=[/tex]
解: 对原式进行分解,得 [tex=15.214x2.643]iw827m0GuJXkG33qVP/q5e5SXTy1CBVfXnB2SCiYDx/UYhMdS4lfWBFMT3kRIi+fsJD4Lk1CTT41H4IT3/Le5Yj4+KrGCxgnXMQB8MK7pbY=[/tex]则[tex=31.857x2.786]fSL60hixiUzNhNkyTGQLpLV3J0JVEUg1dOKCA6eDhPsMOITee36OR+agPy8LsEJ/syzyk1tLWWG6aizsdmaHl9sHLa6lB08V+fIA0nJv9OEv3g1R9GsaT/7+di6yUJZc35Dfd3Szu3ekJU7qlpgr2JYMhxXx+zknLY70SOJ4gTX1c5++avVzaTcCUJ/zhKEki4aUvUlwSQYOlwiODMKP7A==[/tex][查表可得]另解:根据留数定理[tex=3.714x1.143]D8Zz2oOikfnbxitkHB2uhQ==[/tex] 和 [tex=3.714x1.143]AizQ2zoazAntSTmRYlqC6w==[/tex]是原式的一级极点[tex=25.643x15.929]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[/tex]
举一反三
- 求下列函数的 Laplace 逆变换:[tex=7.0x2.429]sMR63Gd/hhMniuOXbiZJxqWFu2pDeyQkBIlZsnfl7Hw=[/tex].[br][/br]
- 试利用Laplace变换的性质求下列函数的Laplace变换。[br][/br][tex=3.357x1.357]2vr2aprfE0f//o6pHWZIXA==[/tex]
- 求下列函数的Z逆变换：[tex=9.714x2.429]H0r7HOEro2H3zl08F2vslFubFPjNpm2KpFVcwteeSMk=[/tex]
- 求下列函数的Z逆变换：[tex=8.714x2.786]CFr2sj528u8n+jtkEi1bXp293b3uuMdg6SKWXNlFZtJ8K2B6kiW9STJZufX0ifHL[/tex]
- 求下列函数的Laplace逆变换．求下列函数的Laplace逆变换．求下列函数的Laplace逆变换．
内容
- 0
试利用Laplace变换的性质求下列函数的Laplace变换。[tex=9.714x2.786]EsyEn7hHZ8RJ2i5cVNU6dYEToOTB+dZdfrYIQteCKi5CXSMsdzU5yF2Vle7y7zSnYESumnUTTeKpQO9HyTIiO6EVpbkc6oi1h5zopQHF/tyRfeZjzeNxx3xcqUCZsaWW[/tex]
- 1
求下列函数的拉普拉斯变换。[br][/br][tex=4.071x1.5]M1NbXW1pRu5C4uTrtfeM3PFrc+FzQBAsbT1Ez+DCrDc=[/tex]
- 2
利用定理6.1和定理6.2，求下列函数的Laplace逆变换：[tex=5.071x2.429]7yAspt9kTXByZXMBZNkl2vqUorX5v8t9LkvTctPAkIg=[/tex].
- 3
求下列函数的 Fourier 变换:[br][/br][tex=11.857x3.357]ACpG7W/lXiEwdW69ASBj8/2YlnttL4SSB5wR8px8LphWGttxXBYV0fE1rrh0lXWpkFbqZB82UnpfKqC9jHUoxKHHU2+BbpwKDlziCwZLVTBehNLVnOAY+6zdPYRHn6gs[/tex]
- 4
求下列函数的拉氏变换。 [tex=10.0x1.5]W8o6Y2GRzjDg1ptfPRp0X5nJlb6HukMnjsuODFzbgIxPbBqYzsJQIeLmetq/KwJK[/tex];[br][/br]