Question

Find the first time after release that the string is 70 cm

Answer 1

Given: A function representing the length of the string after t seconds-

$L=80+30cos(\pi t)$

Required: To determine the first time after release that the string is 70 cm.

Explanation: The given function is-

$L=80+30cos(\pi t)$

Substituting L=70 as follows-

$70=80+30cos(\pi t)$

Further solving for t as-

$\begin{gathered} cos(\pi t)=-\frac{1}{3} \\ \pi t=cos^{-1}(-\frac{1}{3}) \\ t=\frac{1.91063}{\pi} \end{gathered}$

Substituting the value of pie and solving gives-

$t=0.6084\text{ seconds}$