Question

Find the laplace transform of the function 3 cos h5t - 4 sin h5t

Answer 1

Answer:

(3s-20)/(s²-25)

Step-by-step explanation:

laplace transform of cos hat is s/(s²-a²)

similarly for sin hat is a/(s²-a²)

so,

3cos h5t-4sin h5t=(3(s)/(s²-a²))-((4*5)/(s²-25))

                        =(3s/s²-25)-(20/s²-25)

                        =(3s-20)/(s²-25)

I think this is the final answer

Answer 2

Answer:

Step-by-step explanation:

3cosh5t - 4sinh5t

3L(cosh5t) -4L(sinh5t)

= 3(s/s²-5²)-4(5/s²-5²)

( As, L(coshat)= s/s²-a²; a=5 and similarly , L(sinhat)= a/s²-a²)

=3(s/s²-25) - 4(5/s²-25)

=(3s/s²-25) - (20/s²-25)

=3s-20/s²-25.

Done

(After taking the LCM, the term "s²-25" will become the denominator, as a common term)