Answer:
[tex]t \approx 0.202\,s[/tex]
Step-by-step explanation:
The expression that models the motion of pendulum is given by:
[tex]p(t) = -5\cdot \cos (2\pi\cdot t) + 5[/tex]
First, time is cleared with algebraic and trigonometric handling:
[tex]-\frac{p(t) - 5}{5} = \cos (2\pi\cdot t)[/tex]
[tex]\cos^{-1}\left(-\frac{p(t)-5}{5} \right) = 2\pi\cdot t[/tex]
[tex]t = \frac{1}{2\pi}\cdot \cos^{-1} \left(-\frac{p(t)-5}{5} \right)[/tex]
Now, all values are replaced and time is finally computed:
[tex]t = \frac{1}{2\pi}\cdot \cos^{-1}\left(-\frac{3.5-5}{5}\right)[/tex]
[tex]t \approx 0.202\,s[/tex]
