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See 'show steps'.

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Find $L\\{\\cos(\\var{a}t)\\}$

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Note: $L\\{\\cos(bt)\\}=\\frac{s}{s^2+b^2}$

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In this example $b=\\var{a}$

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Find $L\\{\\sin(\\var{b}t)\\}$

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Note: $L\\{\\sin(bt)\\}=\\frac{b}{s^2+b^2}$

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In this example $b=\\var{b}$

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Find $L\\{\\cos(\\frac{t}{\\var{a}})+\\sin(\\frac{t}{\\var{b}})\\}$

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Note: $L\\{\\cos(bt)\\}=\\frac{s}{s^2+b^2}$ and  $L\\{\\sin(bt)\\}=\\frac{b}{s^2+b^2}$

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In the first part $b=\\frac{1}{\\var{a}}$ and in the second part $b=\\frac{1}{\\var{b}}$

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You may use a table of Laplace transforms in order to answer the following questions.

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rebelmaths

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