Each time the oscillator passes in the same direction of the equilibrium position, an additional momentum p is given to it in the direction of velocity. What will be the motion of the oscillator and what will be the maximum velocity? The characteristics of the oscillator are known. Consider two limiting cases: 2$\pi\gamma$/$\omega$ $\ll$ 1 and 2$\pi\gamma/\omega\gg$ 1.
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