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The impulse response $h(t)$ of a linear time-invariant continuous time system is given by $h(t)=\exp (-2 t) u(t)$, where $u(t)$ denotes the unit step function.
The output of this system, to the sinusoidal input $x(t)=2 \cos (2 t)$ for all time $t$, is
1. $0$
2. $2^{-0.25} \cos (2 t-0.125 \pi)$
3. $2^{-0.5} \cos (2 t-0.125 \pi)$
4. $2^{-0.5} \cos (2 t-0.25 \pi)$