Question

Starting from the origin, a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy?

1/6s

1/12s

1/3s

1/4s

Solution

1/6s

1 half mv squared space equals space 3 over 4 open parentheses 1 half mv subscript max superscript 2 close parentheses straight A squared straight omega squared space cos squared space ωt space rightwards double arrow 3 over 4 space straight A squared straight omega squared cos space ωt space equals space fraction numerator square root of 3 over denominator 2 end fraction ωt space equals space straight pi divided by 6 space rightwards double arrow space straight t space equals space 1 divided by 6 space sec

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