(a) To sketch a graph of the force exerted by the spring on the block as a function of the block's horizontal position, we can use Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
Since the graph of the spring potential energy is given, we can find the force by taking the negative derivative of the potential energy with respect to the position. The negative sign is because the force is in the opposite direction of displacement.
(b) To calculate the period of oscillation for the block-spring system, we can use the formula:
T = 2π√(m/k)
Where T is the period, m is the mass of the block, and k is the spring constant. In this case, the mass is 0.4 kg and the spring constant can be determined from the graph of potential energy.
(c) To sketch the curve for the kinetic energy of the new block-spring system as a function of the horizontal position, we need to consider that the kinetic energy of the block-spring system is at its maximum when the block passes through the equilibrium position (x = 0). As the block moves away from the equilibrium position, the kinetic energy decreases, reaching zero at the maximum displacement.
Thus, the kinetic energy curve should start at zero, increase as the block moves towards the equilibrium position, reach a maximum at the equilibrium position, and then decrease symmetrically as the block moves away from the equilibrium position.
The sketch should show a symmetric curve with the highest point at the equilibrium position and decreasing values on both sides as the block moves away from equilibrium.
Please note that the accuracy and specifics of the sketches will depend on the actual values and shape of the given graphs, which are not provided in the question.