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A particle executes simple harmonic motion of period 12 s about a…
Question
A particle executes simple harmonic motion of period 12 s about a mean position, starting from rest at one extreme. As it moves toward the mean position, find the time (in seconds) it takes to travel from the point where its displacement is (sqrt(3)/2) of the amplitude to the point where its displacement is half the amplitude.
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Step-by-step solution
Starting from rest at an extreme, x = A cos(wt) with w = 2*pi/12 = pi/6 rad/s.
At x = (sqrt(3)/2)A: cos(wt1) = sqrt(3)/2, so wt1 = pi/6.
At x = A/2: cos(wt2) = 1/2, so wt2 = pi/3.
Time interval = (wt2 - wt1)/w = (pi/3 - pi/6)/(pi/6) = (pi/6)/(pi/6) = 1 s.
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