Question

A mass on a spring moves with simple harmonic motion as shown.

1)Where is the acceleration of the mass most positive?
x = -A
x = 0
x = +A

Answer 1

The acceleration of the mass on the spring is most positive at x = -A.

Step-by-step explanation:

The acceleration of the mass on the spring is most positive at x = -A.

During simple harmonic motion, the acceleration of the mass is given by the equation –amax cos (wt + Ø). The maximum acceleration is amax = Aw², and it occurs at the position x = -A, where x = 0 is the equilibrium position.

Therefore, the acceleration of the mass is most positive when it is at x = -A.

Answer 2

The acceleration of the mass is most positive when the spring is at its maximum negative displacement, which occurs at x = -A.

Step-by-step explanation:

The acceleration of the mass on a spring is most positive when the spring is most compressed or stretched. Since the acceleration is defined as the second derivative of the position, and is proportional to the displacement in simple harmonic motion governed by Hooke's law, it reaches its maximum value when the displacement is at its maximum in the negative direction (x = -A). At this point, the acceleration vector is directed towards the equilibrium position (x = 0), but because the mass is on the negative side (x = -A), the acceleration is considered positive in sign. Contrarily, when the mass passes through the equilibrium point, the acceleration is zero since it's at maximum velocity. At the furthest positive displacement (x = +A), the acceleration is maximum but negative, as it is directed back towards the equilibrium.