A \(0.15 \mathrm{~kg}\) cart on wheels is at rest at the origin of an \(x\) axis between (but not connected to) two relaxed springs aligned along that axis. When the cart is pushed to the left of the origin, the left spring \(\left(k_{1}=4.0 \mathrm{~N} / \mathrm{m}\right)\) is compressed and exerts a force on the cart. When the cart is pushed to the right of the origin, the right spring \(\left(k_{\mathrm{r}}=6.0 \mathrm{~N} / \mathrm{m}\right)\) is compressed and exerts a force on the cart.

(a) Plot the force exerted on the cart as a function of its displacement.

(b) If the cart is given an initial speed of \(4.0 \mathrm{~m} / \mathrm{s}\) at the origin \(x=0\), it might be headed to the left or to the right. How far does it go in each case?

(c) What is the work done on the cart as it moves from \(x=0\) to its extreme right position and from \(x=0\) to its extreme left position? Ignore any friction effects.