Two \(0.500-\mathrm{kg}\) carts are \(100 \mathrm{~mm}\) apart on a low-friction track. You push one of the carts with a constant force of \(2.00 \mathrm{~N}\) directed so that the cart you push moves away from the other cart. Determine the acceleration of the center of mass of the two-cart system whenn(a) the carts do not interact and \((b)\) the carts are connected by a spring of spring constant \(k=300 \mathrm{~N} / \mathrm{m}\).