Answer
After $t = 0$, the next three times the two objects simultaneously pass through the origin are $t = \pi$, $t = 2\pi$, and $t=3\pi$.
Work Step by Step
First,
$x_A = (2.0~m)~sin(4.0t)$
If object A is at the origin, then $x_A = 0$. Therefore;
$x_A = (2.0~m)~sin(4.0t) = 0$
$sin(4.0t) = 0$
$4.0t = n\pi$ (for some integer $n$)
$t = \frac{n\pi}{4.0}$ (for some integer $n$)
Next,
$x_B = (5.0~m)~sin(3.0t)$
If object B is at the origin, then $x_B = 0$. Therefore;
$x_B = (5.0~m)~sin(3.0t) = 0$
$sin(3.0t) = 0$
$3.0t = n\pi$ (for some integer $n$)
$t = \frac{n\pi}{3.0}$ (for some integer $n$)
After $t = 0$, the next three times the two objects simultaneously pass through the origin are $t = \pi$, $t = 2\pi$, and $t=3\pi$.
