Introduction:
Under forced oscillation, a particle is subjected to an external driving force that causes it to oscillate with a frequency and amplitude determined by the force. The phase of the harmonic motion of the particle refers to the position of the particle within its oscillation cycle, while the phase of the driving force refers to the position of the force within its own oscillation cycle.

Difference in Phase:
The correct answer is option 'B', which states that the phase of the harmonic motion of the particle and the phase of the driving force are different. This means that the particle and the driving force are not in sync with each other in terms of their positions within their respective oscillation cycles.

Explanation:
When a particle undergoes forced oscillation, it is influenced by an external driving force that applies a periodic force on the particle. This driving force can be represented by a sinusoidal function, such as F(t) = F0 sin(ωt), where F0 is the amplitude of the force and ω is the angular frequency.

The particle's harmonic motion, on the other hand, can be described by a sinusoidal function of the form x(t) = A sin(ωt + φ), where A is the amplitude of the particle's motion and φ is the phase constant.

Since the particle and the driving force have different equations representing their motion, their phases will generally not be the same. This means that at a given time t, the particle may be at a different position within its oscillation cycle compared to the driving force.

Example:
For example, suppose we have a simple harmonic oscillator with a driving force given by F(t) = F0 sin(ωt) and a particle undergoing harmonic motion described by x(t) = A sin(ωt + φ). If we set t = 0, we can compare the positions of the particle and the driving force.

At t = 0, the particle's position is given by x(0) = A sin(φ), while the driving force's position is given by F(0) = F0 sin(0) = 0. This demonstrates that the particle and the driving force are not in phase with each other.

Conclusion:
In summary, under forced oscillation, the phase of the harmonic motion of the particle and the phase of the driving force are different. This means that the particle and the driving force are not in sync with each other in terms of their positions within their respective oscillation cycles.