Question

determine the laplace transform of the function sinh4t+cosh3t

Answer 1

maths for this is whay too difficult to type out, that;s why they made tables for them:
http://tutorial.math.lamar.edu/pdf/Laplace_Table.pdf

Answer 2

howd u go dude, does that make sense? @STONEBRIDGE ?

Answer 3

First, Stonebridge, could you tell me how much experience you've had so far with Laplace Transforms?

If you'll look at the table of Laplace Transforms that Jack has brought to our attention, you'll see in the middle left of the table the time function sinh (at) (the hyperbolic sine of (a times t)). Right next to it is the appropriate Laplace Transform: \[\frac{ a }{s^2-a^2 }\]

Answer 4

Thus, the Laplace transform of sinh 4t is \[\frac{ 4 }{ s^2-4^2 }\]

Answer 5

Now look in the same table for the Laplace transform of cosh a*t. Apply this formula to the given function cosh 3t.

Thus, the Laplace transform of sinh 4t*cosh 3t is the sum of two individual Laplace transforms: that for sinh 4t and that for cosh 3t.