# Dirac delta forcing of a harmonic oscillator

Is it possible to solve this differential equation: $$\ddot{x}(t)+\omega^2x(t)=k\delta(t)$$ where $k$ is a constant and $\delta(t)$ the Dirac delta function? Is it possible alternatively, to know something about the spectrum $X(\omega)$ of $x(t)$ without solving the equation? Thanks

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