Topic: Oscillatory Motion
Concepts: Mass-spring system, Power

Solution:

Recall the instantaneous power delivered to the mass is $P=Fv$ where $F$ is the spring force and $v$ is the velocity of the mass.

• At $t=0$, there is no force on the mass so $P=0$.
• At $t=T/8$, the force and velocity are pointing in opposite directions so $P<0$.
• At $t=T/4$, the mass is at rest so $P=0$.
• At $t=3T/8$, the force and velocity are pointing in the same direction so $P>0$.
• At $t=T/2$, there is no force so $P=0$.

Thus, power delivered is first maximized at $t=3T/8$ so the answer is D.