The function d=11cos6t describes a simple harmonic motion, where d is the distance(in meters) an object travels in t seconds. What is the time required for one complete cycle?
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It would be 2pi/6 because period (1 oscillation) = 2pi/b
To find the time required for one complete cycle in simple harmonic motion, we need to find the period of the motion. The period is the time it takes for the object to complete one full cycle or oscillation.
In this case, the given function is d = 11cos(6t), where d is the distance and t is the time in seconds.
The general equation for simple harmonic motion is d = A * cos(Bt), where A represents the amplitude (maximum distance from the mean position) and B represents the frequency (number of complete cycles per unit time).
Comparing the given function d = 11cos(6t) with the general equation, we can deduce that the amplitude A is 11 and the frequency B is 6.
The period (T) is given by the formula T = 1 / B.
Substituting the value of B into the formula, we get T = 1 / 6.
Therefore, the time required for one complete cycle is 1 / 6 seconds or approximately 0.1667 seconds.