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If a simple harmonic motion is described by x = 3 cos(πt), starting from t = 0 s, what is the first occurrence of a value of t for which x = 0? Assume SI units.

User Dezhi
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1 Answer

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Answer:

The first occurence of t for which x = 0 is t = 0.5.

Explanation:

The harmonic motion is described by the following equation.


x(t) = 3cos(\pi t)

What is the first occurrence of a value of t for which x = 0?

This is t when
x(t) = 0. So


x(t) = 3cos(\pi t)


3cos(\pi t) = 0


cos(\pi t) = (0)/(3)


cos(\pi t) = 0

The inverse of the cosine is the arcosine. So we apply the arcosine function to both sides of the equality.


\arccos{cos(\pi t)} = \arccos{0}


\pi t = (\pi)/(2)


t = (\pi)/(2 \pi)


t = (1)/(2)


t = 0.5

The first occurence of t for which x = 0 is t = 0.5.

User Andrew Faulkner
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