Final answer:
The output of an LTI system with a given transfer function and an exponential input is found using the Laplace transform and the convolution theorem. The impulse response of the system is calculated from the transfer function, after which the output is determined by convolving the input signal with the impulse response.
Step-by-step explanation:
You have queried about the output of a Linear Time-Invariant (LTI) system given the transfer function H(jω) = 1 / (2 + jω) and the input x(t) = e^(-t) u(t). To find the output of an LTI system, we can use the convolution theorem, which relates the input, output, and transfer function in the frequency domain. However, since this problem involves an LTI system and an exponential input signal, we can also approach it using the Laplace transform
The Laplace Transform of the input signal x(t) = e^(-t) u(t) is X(s) = 1 / (s + 1). We can find the system's impulse response by taking the inverse Laplace transform of the transfer function H(s), where s = jω. After finding the impulse response h(t), the output y(t) can be obtained by convolving x(t) and h(t).
To solve this problem thoroughly and obtain the precise output signal y(t), we would perform these steps and calculate the convolution integral, but it's important not to confuse this scenario with simple harmonic motion or superposition of waves which have been mentioned in the reference information but are not directly applicable to solving this specific problem.