The image shows one complete cycle of a mass on a spring in simple harmonic motion.   which describes the system at point d? a. the velocity has the maximum upward value because the acceleration upward is at a maximum. b.the net force is at a maximum in the downward direction, so the velocity begins to decrease. c.the velocity is zero because the net force is zero. d. the net force is zero, so the acceleration is zero.

D. The net force is zero, so the acceleration is zero

Explanation:

In a simple harmonic motion, velocity and acceleration are out-of-phase as follows:

- When the displacement is zero (so, when the spring is in equilibrium position), the acceleration is zero, because the force is zero. In fact, the force is given by Hook's law:

So, when x=0, F=0, and the acceleration is also zero according to Newton's second law:

Instead, the velocity is maximum. In fact, the total mechanical energy (sum of kinetic and elastic potential energy) is constant, and since the elastic potential energy:

is zero at x=0, this means that the kinetic energy is maximum. But the kinetic energy is

and so, the velocity is also maximum.

- When the displacement is maximum, it is the opposite: the acceleration is maximum (because x is maximum, so the force is maximum), while the velocity is zero, because the elastic potential energy is maximum and so the kinetic energy is zero).

At point D, we are in the first situation (the spring is passing its position of equilibrium, so x=0), therefore the net force is zero and the acceleration is zero.

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