Amass is undergoing simple harmonic motion. when its displacement is 0, it is at its equilibrium position. at that moment, its speed is and its acceleration is

0, 0
max, max
0, max
max, o

Its speed is maximum and its acceleration is zero

Explanation:

- Concerning the speed:

In a simple harmonic motion, the speed can be determined through the law of conservation of energy. In fact, we have that the total mechanical energy of the system, which is sum of elastic potential energy U and kinetic energy K, is constant:

where k is the spring constant, x is the displacement, m is the mass and v is the speed.

We see that when the displacement is 0, x = 0: this means that the elastic potential energy U is also 0, therefore the kinetic energy K is maximum, and so the speed v is also maximum.

- Concerning the acceleration:

According to Newton's second law, the acceleration of the system is proportional to the net force:

the net force is just the restoring force of the spring, given by Hooke's law:

So, the acceleration is

and we see that when the displacement is zero, x = 0, and so the acceleration is also zero.

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