Question

Solve the Laplace transform for f(t)=sin(2t)+cos(2t).

a) F(s)=2s/s²+4 + s​/s²+4
b) F(s)=s/s²−4 + 2s /s²−4
c) F(s)=2s/s²−4+s/s²+4
d) F(s)=s/s²−4+2s/s²−4​

Solve the Laplace transform for f(t)=e−atcos⁡(bt)f(t)=e^−at cos(bt)

a) F(s)=s+a / (s+a)²+b²
b) F(s)=s−a / (s−a)²+b²
c) F(s)=s−a / (s+a)2+b²
d) F(s)=s+a / (s−a)²+b²

Answer 1

The Laplace transform of f(t) = sin(2t) + cos(2t) is F(s) = (3s) / (s^2 + 4).

Step-by-step explanation:

To solve the Laplace transform for f(t) = sin(2t) + cos(2t), we can use the linearity property of the Laplace transform. The Laplace transform of sin(2t) is (2s) / (s^2 + 4) and the Laplace transform of cos(2t) is s / (s^2 + 4). Therefore, the Laplace transform of f(t) = sin(2t) + cos(2t) is:

F(s) = (2s) / (s^2 + 4) + s / (s^2 + 4) = (2s + s) / (s^2 + 4) = (3s) / (s^2 + 4)

Therefore, the correct answer is option a) F(s) = (3s) / (s^2 + 4).