How many times is the transit time of the oscillating point of the first half of the amplitude less than the transit

How many times is the transit time of the oscillating point of the first half of the amplitude less than the transit time of the second half? Oscillations follow the law x = Asinwt

Data: the law of oscillation of the specified point: x = A * sinωt.

1) The duration of the passage by the specified point of the first half of the amplitude: A / 2 = x = A * sinωt1; 0.5 = sin (2Π / T * t1); Π / 6 = 2Π / T * t1; t1 = Π / 6 * T / 2Π = T / 12.

2) The duration of the passage of the second half of the amplitude: t2 = T / 4 – x = T / 4 – T / 12 = T / 6.

3) The ratio of time intervals: t2 / t1 = (T / 6) / (T / 12) = 12/6 = 2 p.

Answer: The point passes the first half of the amplitude 2 times faster.



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