$24)$A $3\mathrm{.}50kg$ object hangs, at rest, on a $1\mathrm{.}10m$ long string attached to the ceiling. A $103g$ object is fired with a speed of

$15\frac{m}{s}$ at the $3\mathrm{.}50kg$ object, and the two objects collide and stick together in an inelastic collision. Write an equation for

the motion of the system after the collision. Assume air resistance is negligible. $($Assume the collision occurs at $t=0.$ Let $$

be the angle between the initial position of the hanging mass and its position at time $t.$ In your equation, let angles be in

radians and time be in seconds. Do not include units in your answer. Use the following as necessary: $t.)$

$(t)=,$rad