Final answer:
The energy dissipated by damping in a block on a spring is replaced by the applied sinusoidal force, which acts to continuously replenish the energy lost due to the damping force. The correct option is D.
Step-by-step explanation:
The energy dissipated by damping in a damped oscillator such as a block on a spring with air friction is compensated by the applied sinusoidal force. The role of this force is to replenish the energy that is lost due to damping effects, which typically convert mechanical energy into thermal energy.
The spring force is conservative and does not add energy to the system; it merely transfers energy between potential and kinetic forms within the system.
The block's initial kinetic energy can only provide energy temporarily and would eventually be depleted without an external energy source. The damping force itself is responsible for the dissipation of energy, not the provision of it. Option D. is the correct one.