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What is the maximum velocity and maximum acceleration of a particle in Simple Harmonic Motion (SHM) in terms of amplitude (A) and angular frequency (w)?

a) Velocity: A * w, Acceleration: A * w^2
b) Velocity: A * w^2, Acceleration: A * w
c) Velocity: A, Acceleration: A * w^2
d) Velocity: A * w^2, Acceleration: A

User Ygesher
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1 Answer

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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.

User Graney
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