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Dartmouth Extended Laplace Tables -- Not general enough? item26.a
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[QUOTE="collinsmark, post: 5407708, member: 114325"] I'm actually a little suspicious that the entry 26a in the table might not even be correct at all. Unless I'm making a large mistake myself, here is my logic: I suspect that the constant [itex] \alpha [/itex] should have dimensionality of [itex] \frac{1}{[\mathrm{time}]} [/itex]. (Again, that is if I'm not mistaken). If so, then one of the terms in 26a doesn't make sense to me: in particular, the part of term that is [itex] \frac{\alpha}{\omega_n} - \zeta \omega_n [/itex]. [itex] \omega_n [/itex] also has units of [itex] \frac{1}{[\mathrm{time}]} [/itex]. That makes [itex] \frac{\alpha}{\omega_n} [/itex] dimensionless (if I'm correct about [itex] \alpha [/itex]), and [itex] \zeta [/itex] is dimensionless. But that gives [itex] \zeta \omega_n [/itex] dimensionality of [itex] \frac{1}{[\mathrm{time}]} [/itex]. So that operation is subtracting a [itex] \frac{1}{[\mathrm{time}]} [/itex] value from a dimensionless number. With that I conclude (or at least suspect) that something doesn't look right with 26a to me. [/QUOTE]
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Dartmouth Extended Laplace Tables -- Not general enough? item26.a
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