Question

An object that is oscillating on a spring is given by the equation x = (10.0 cm) cos[(6.00 s-1)t]. At what value of t after t = 0.00 s is the cart first located at x = 8.00 cm?

Answer 1

Answer:

$t=0.0107\ \text{s}$

Explanation:

$x=10\cos(6t)$

Now $x=8\ \text{cm}$

Substituting the value of $x$ in the equation we get

$8=10\cos6t$

$\Rightarrow 0.8=\cos6t$

$\Rightarrow \cos^{-1}0.8=6t$

$\Rightarrow t=\dfrac{\cos^{-1}0.8}{6}$    the values here are used found in radians

$\Rightarrow t=0.0107\ \text{s}$

So, at $t=0.0107\ \text{s}$ the value of $x=8\ \text{cm}$.