Final answer:
The velocity of a particle executing linear simple harmonic motion at the equilibrium position is the maximum velocity, Vmax. Option B is correct.
Step-by-step explanation:
The student has asked about the velocity of a particle executing linear simple harmonic motion (SHM) at a particular point. The velocity of a particle in SHM is maximum when it passes through the equilibrium position, where the potential energy is zero, and the kinetic energy is maximum.
Using the principle that kinetic energy K is given by K = 1/2mv², at the equilibrium position x = 0, all the energy is kinetic, so the velocity v should be the maximum velocity Vmax. Therefore, when a particle crosses a particular point in its shortest time period, implying it is at equilibrium, its velocity will not be zero, Vmax/2, or Vmax²/√2, but rather the maximum velocity Vmax.
The velocity of a particle executing linear Simple Harmonic Motion (SHM) can be determined based on its time period.
The velocity is maximum when the particle crosses the equilibrium position. Therefore, the answer is B. Vmax, as the maximum velocity occurs when the particle is at the equilibrium position.
It is important to note that the velocity of the particle is constantly changing throughout its motion, but it reaches its maximum value when it crosses the equilibrium position.