Question

Rana writes a summary about a mass on a spring in simple harmonic motion as it moves upward from the equilibrium position toward the maximum positive displacement. as the mass moves upward, the velocity is positive and decreasing while the acceleration is negative and decreasing. what error did rana make? the velocity should be negative, not positive. the acceleration should be positive, not negative. the velocity should be increasing, not decreasing. the acceleration should be increasing, not decreasing.

Answer 1

Answer:

The magnitude of acceleration should be increasing.

Velocity is positive as the mass is moving towards the maximum positive displacement. Velocity would be decreasing. Acceleration is negative as velocity is decreasing. Additionally, the magnitude of acceleration would be increasing (becomes more negative.)

Explanation:

As the mass in this question moves upwards, the displacement of this mass is becoming more positive. Hence, the velocity of this mass would be positive.

In a simple harmonic motion, velocity is:

• maximized at the equilibrium position (where displacement is $0$,) and
• $0$ when displacement is maximized.

The mass in this question is moving from $0$ displacement (where velocity is maximized) towards maximum displacement (where velocity is $0$.) Thus, the velocity of the mass would be decreasing.

Since the velocity of this mass is decreasing, the acceleration of this mass would be negative. In a simple harmonic motion, acceleration is:

• $0$ at the equilibrium position, and
• maximum when displacement is maximized, but opposite to the direction of displacement.

The mass in this question is moving from the equilibrium position (where acceleration is $0$) towards maximum displacement (where acceleration is most negative.) Thus, the magnitude of the acceleration of this mass would be increasing, and the acceleration of the mass would become more negative.