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The column headings from left to right are z of t and Z tilde.

- z of t, A cosine omega t. Z tilde, A.

- z of t, A cosine of omega t plus phi sub 0 right parenthesis. Z tilde, A e to the power of start expression j phi sub 0 end expression.

- z of t, A cosine of start expression omega t plus beta x plus phi sub 0 end expression. Z tilde, A e to the power of start expression j left parenthesis beta x plus phi sub 0 right parenthesis end expression.

- z of t, A e to the power of negative alpha x cosine left parenthesis omega t plus beta x plus phi sub 0 right parenthesis. Z tilde, A e to the power of start expression negative alpha x end expression e to the power of start expression j left parenthesis beta x plus phi sub 0 right parenthesis.

- z of t, A sine omega t. z tilde, A e to the power of start expression start fraction negative j pi over 2 end fraction end expression.

- z of t, A sine of omega t plus phi sub 0. Z tilde, A e to the power of start expression j left parenthesis phi sub 0 minus start fraction pi over 2 end fraction end expression.

- z of t, derivative z of t. z tilde, j omega Z tilde.

- z of t, derivative A cosine of omega t plus phi sub 0. Z tilde, j omega A e to the power of start expression j phi sub 0 end expression.

- Z of t, integral z of t d t. Z tilde, start fraction 1 over j omega end fraction Z tilde.

- Z of t, integral A sine of omega t plus phi sub 0 d t. Z tilde, start fraction 1 over j omega end fraction A e to the power of start expression j left parenthesis phi sub 0 minus pi over 2 right parenthesis end expression.