Final answer:
The maximum velocity of a particle in Simple Harmonic Motion is given by the amplitude times the angular frequency (Umax = Aω), and the maximum acceleration is the product of the amplitude and the square of the angular frequency (amax = Aω²).
Step-by-step explanation:
In Simple Harmonic Motion (SHM), a particle's maximum velocity (∆max) and maximum acceleration (amax) can be expressed in terms of the particle's amplitude (A) and angular frequency (ω). The maximum velocity of a particle is given by the product of its amplitude and angular frequency, Umax = Aω. Since the sine function varies from -1 to +1, this maximum velocity occurs when the sine function is at either +1 or -1, which is at the equilibrium position where x = 0.
The maximum acceleration, however, occurs when the restoring force is the greatest, which is at the maximum displacement from the equilibrium position, meaning at x = ±A. Hence, the maximum acceleration of the particle in SHM can be calculated using the formula amax = £ω². This acceleration is directed towards the equilibrium position, highlighting the restoring nature of the force involved in SHM.