Question

What is the first time the pendulum reaches 3.5 cm from the place it was released?

P(t)= -5cos(2piT)+5

How many seconds ?

Answer 1

`t \approx 0.202\,s`

Explanation:

The expression that models the motion of pendulum is given by:

`p(t) = -5\cdot \cos (2\pi\cdot t) + 5`

First, time is cleared with algebraic and trigonometric handling:

`-(p(t) - 5)/(5) = \cos (2\pi\cdot t)`

`\cos^(-1)\left(-(p(t)-5)/(5) \right) = 2\pi\cdot t`

`t = (1)/(2\pi)\cdot \cos^(-1) \left(-(p(t)-5)/(5) \right)`

Now, all values are replaced and time is finally computed:

`t = (1)/(2\pi)\cdot \cos^(-1)\left(-(3.5-5)/(5)\right)`

`t \approx 0.202\,s`