A 2-m wire fixed at both ends is vibrating in its fundamental mode. The tension in the wire is 40 N and the mass of the wire is 0.1 kg. At the midpoint of the wire, the amplitude is 2 cm.

(a) Find the maximum kinetic energy of the wire.

(b) At the instant the transverse displacement is given by (0.02 m) sin (px/2), what is the kinetic energy of the wire?

(c) At what position on the wire does the kinetic energy per unit length have its largest value?

(d) Where does the potential energy per unit length have its maximum value?