Final answer:
To find the time function of the given Laplace transform, factorize the denominator, apply partial fraction expansion, and find the inverse Laplace transform. The unit step response of a system is found by setting the input signal as a unit step function and finding the inverse Laplace transform of the transfer function.
Step-by-step explanation:
To find the time function of the given Laplace transform, we can use partial fraction expansion. Firstly, we need to factorize the denominator of the Laplace transform.
The denominator factors as follows: (s+2)(s^2+5s+11). Then, we can express the given Laplace transform as the sum of its partial fractions: F(s) = A/(s+2) + (Bs+C)/(s^2+5s+11).
Next, we need to solve for the unknown constants A, B, and C. Once we know these values, we can find the inverse Laplace transform of each term. After performing the inverse Laplace transform, we obtain the time function of the given Laplace transform.
The unit step response of a system is given by the inverse Laplace transform of its transfer function with the input signal set as a unit step function. This represents the system's output when it is subjected to a sudden change in input from zero to one at t=0.
Therefore, to find the unit step response of the given Laplace transform, we need to find the inverse Laplace transform of the transfer function and set the input signal as a unit step function (1/s).