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The displacement equation of SHM is y = 0.5 (sin 3πt + √3 cot 3πt). Find Amplitude, Angular frequency, Period of oscillation, velocity and acceleration. |
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Answer» y = 0.5 (sin 3πt + √3 cot 3πt) y = 0.5 x 2 ( \(\cfrac12\) sin 3πt + \(\cfrac{\sqrt3}2\) cot 3πt) y = 1 ( cot \(\cfrac{\pi}3\) sin 3πt - sin \(\cfrac{\pi}3\) cot 3πt) y = sin( 3πt + \(\cfrac{\pi}3\)) Comparing equation y = A sin (ωt + θ) Then amplitude A = 1 Angular frequency ω = 3π rad/sec Time period T = \(\cfrac{2\pi}ω\) T = \(\cfrac{2\pi}{3\pi}\) T = \(\cfrac23\) sec Acceleration a = Aω2 = 1 x (3π)2 a = 9π2 m/s2 Velocity v = Aω v = 1 x 3π v = 3π m/s |
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