Angular frequency is crucial in determining the energy of an oscillating system. The total energy of the system is often expressed in terms of angular frequency. For example, the total mechanical energy of a system in SHM is given by ET = 1/2 m * omega² * x0², where m is mass, omega is angular frequency, and x0 is the amplitude. This formula illustrates the direct proportionality between the square of the angular frequency and the total energy of the system. Hence, a higher angular frequency implies a higher energy of oscillation, assuming the mass and amplitude remain constant.

Yes, the phase angle can indeed be negative. A negative phase angle signifies that the oscillating system started its motion at a point corresponding to a negative angle on the unit circle or, in other words, it indicates the direction of the oscillation. For instance, in the context of a cosine function, a negative phase angle means the oscillation began at a point below the x-axis on the unit circle. It's essential to recognise that a negative phase angle essentially represents a delay in the start of the oscillation relative to the reference phase.

To determine the phase angle in real-time as the particle oscillates, we typically use sensors or detectors to measure the displacement and velocity of the particle at a specific point in time. By applying these values to the equations of motion or energy equations of SHM, we can calculate the instantaneous phase angle.

Indeed, using radians offers several distinct advantages. Firstly, it simplifies mathematical expressions and calculations, as many mathematical functions, especially trigonometric ones, have coefficients and constants that are tailored for radian measures. Secondly, it provides a direct correlation between the angular displacement and the length of the corresponding arc on the unit circle, facilitating an intuitive grasp of oscillatory behaviour. Lastly, in advanced physics and mathematics, where calculus often plays a significant role, radian measures are typically more convenient and lead to more straightforward, less complex expressions and formulas.

The use of radians profoundly impacts the graphical representation of SHM. When radians are employed, the x-axis typically represents the angular displacement in radians, while the y-axis represents the amplitude of the motion. It provides a clear and concise visualisation of the oscillation, making it easier to interpret the phase and amplitude at various points throughout the cycle. Also, with radians, every point on the graph can be directly associated with a specific angular displacement, which aids in an intuitive understanding of the oscillation's characteristics and behaviour.