Answer
(a) The magnitude of the force on the cart is $2kx$
(b) $\omega = \sqrt{\frac{2k}{m}}$
Work Step by Step
(a) When the cart is displaced a distance $x$ from the equilibrium position, a force of $kx$ from each spring is exerted on the cart and this force is directed toward the equilibrium position. The magnitude of the net force on the cart is $2kx$.
(b) Since the magnitude of the force on the cart is $2kx$, the equivalent spring constant of the system is $2k$. We can find the angular frequency $\omega$:
$\omega = \sqrt{\frac{2k}{m}}$
