The times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position are 78.10s, 61.71s, and 42.41s respectively
Explanation:Given the equation:
[tex]h=7\cos(\frac{\pi}{3}t)[/tex]Make t the subject:
[tex]\begin{gathered} \frac{h}{7}=\cos(\frac{\pi}{3}t) \\ \\ \cos^{-1}(\frac{h}{7})=\frac{\pi}{3}t \\ \\ t=\frac{3}{\pi}\cos^{-1}(\frac{h}{7}) \end{gathered}[/tex]We now substitute h = 1, 3 and 5
[tex]\begin{gathered} t=\frac{3}{\pi}\cos^{-1}(\frac{1}{7})=78.10 \\ \\ t=\frac{3}{\pi}\cos^{-1}(\frac{3}{7})=61.71 \\ \\ t=\frac{3}{\pi}\cos^{-1}(\frac{5}{7})=42.41 \end{gathered}[/tex]The times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position are 78.10s, 61.71s, and 42.41s respectively
