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

Question

asked Dec 7, 2023 53.5k views

1 Answer

Nouman · Answer 1 · 2023-12-11T15:34:51+0000

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-

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

Substituting the value of pie and solving gives-

$t=0.6084\text{ seconds}$