The oscillatory motion of a point is described by the equation x = 20sin16Пt.
| April 30, 2021 | education
The oscillatory motion of a point is described by the equation x = 20sin16Пt. Write the equation for the dependence of speed and acceleration on time. find the speed 1/64 after the moment t = 0
By definition, the speed is a derivative of the law of motion in time, and the acceleration is the second derivative, then:
v (t) = (20sin (16πt) ‘= 20 * 16 * π * cos (16πt).
v (1/4) = 320πcos (16π / 64) = 320πcos (π / 4) = 320π√2 / 2 = 160√2π.
a (t) = (320π * cos (16πt)) = -5120π ^ 2 * sin (16πt).
Answer: v (t) = 320π * cos (16πt), a (t) = -5120π ^ 2 * sin (16πt).
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