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A continuous-time system that is initially at rest is described by dy(t)/dt + 3y(t) = 2x(t), where x(t) is the input voltage and y(t) is the output voltage. The impulse response of the system is

1. 3e⁻²t
2. (1/3)e⁻²t u(t)
3. 2e⁻³t u(t)
4. 2e⁻³t

Correct answer: 2e⁻³t u(t)

Solution

The correct option represents the impulse response derived from the system's differential equation, which can be solved using the Laplace transform. The term 'u(t)' indicates that the response is causal, and the exponential decay factor '2e^(-3t)' reflects the system's dynamics, confirming it matches the form of the impulse response.

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