Which graph can represent the kinetic energy of the block as a function of x?

Question

A block oscillates without friction on the end of a spring as shown. The minimum and maximum lengths of the spring as it oscillates are, respectively, x_min and x_max. The graphs below can represent quantities associated with the oscillation as functions of the length x of the spring.

Which graph can represent the kinetic energy of the block as a function of x? 

(A) A 

(B) B 

(C) C 

(D) D 

(E) E

Answer 1

Correct option (D) D

The box momentarily stops at x(min) and x(max) so must have zero K at these points. The box accelerates the most at the ends of the oscillation since the force is the greatest there. This changing acceleration means that the box gains speed quickly at first but not as quickly as it approaches equilibrium. This means that the K gain starts of rapidly from the endpoints and gets less rapid as you approach equilibrium where there would be a maximum speed and maximum K, but zero force so less gain in speed. This results in the curved graph.