Question

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.

Answer 1

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.