Mathematics, 26.12.2020 20:40, breeball

A particle moves about a fixed point O in a straight line AOA' . A SHM of periodic time $\frac{2\pi }{ω}$ and amplitude OA=a. After time from reaching the end A, the particle receives a blow in the direction of motion which increases the magnitude of its velocity by the amount ωa. Show that the new amplitude is $a\sqrt{3}$

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A particle moves about a fixed point O in a straight line AOA' . A SHM of periodic time and amplitude OA=a. After time from reaching the end A, the particle receives a blow in the direction of motion which increases the magnitude of its velocity by the amount ωa. Show that the new amplitude is