In the figure below, a mass is oscillating on a spring. Which of the following statements are true?

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BlackTom AI · Accepted Answer

To approach this question, let’s recall the key physics: a mass on a spring experiences a net (restoring) force directed toward the equilibrium position. This force is proportional to the displacement from equilibrium and always points opposite to the displacement. In a visual sequence of frames, the direction of the net force at a given frame depends on where the mass is relative to equilibrium and the direction it is moving (though the force direction itself is set by position, not velocity). With that in mind, we’ll evaluate each statement.

Option A: In the third frame from the left, the ball is experiencing a net force to the left.
- If the mass is to the right of equilibrium (displaced to the right) the restoring force should act to the left (toward equilibrium). This would make a leftward net force plausible in a frame where the mass lies to the right of center. Conversely, if the mass were to the left of equilibrium, the restoring force would be to the right. The statement could be correct if, in the third frame, the mass is indeed to the right of equilibrium. Without the exact frame-by-frame positions, we can’t confirm definitively, but it is a plausible scenario when the displacement is to the right.

Option B: In the first frame from the left, the ball is experiencing no net force.
- In simple harmonic motion, the net force is zero only at the instant of equilibrium (displacement zero). If the first frame shows the mass exactly at equilibrium, then the net force would be zero; however, it is uncommon to have exactly the equilibrium position shown as a nonzero displacement in a typical frame sequence. Without explicit frame data, this claim is uncertain and often incorrect in a sequence where the mass visibly occupies a displaced position. Generally, the restoring force is nonzero except at the precise equilibrium point.

Option C: In the fourth frame from the left, the ball is experiencing a net force to the right.
- This mirrors the logic of A but with the opposite direction. If in the fourth frame the mass is displaced to the left of equilibrium, the restoring force would point to the right. As with A, the correctness hinges on the actual displacement in that frame. If the frame indeed shows the mass on the left side, a rightward net force is exactly what we expect.

Option D: Both A and C are correct
- Given the preceding analyses, if in the third frame the mass lies to the right of equilibrium (net force to the left) and in the fourth frame the mass lies to the left of equilibrium (net force to the right), then both A and C would be correct simultaneously. Since the restoring force in SHM always points toward equilibrium, it is perfectly reasonable for A and C to both be true in two different frames of the oscillation.

In summary, the correctness of A and C depends on the specific displacements shown in the third and fourth frames. If those frames place the mass to the right of equilibrium (A) and to the left of equilibrium (C) respectively, then both statements are correct, which makes option D the accurate overall choice. B is less consistent with typical SHM sequences unless the mass is exactly at equilibrium in the very first frame, which is a special-case scenario and not guaranteed by the plot. The key misconception to avoid is assuming the net force is zero except at a clearly labeled equilibrium frame; in a generic oscillation sequence, there are multiple frames where the net force is nonzero and directed toward center.}

PHYS 2305 Spring 25 Lin Quiz 07 - Chapter 9 (9.4-9.6) and Chapter 10 (10.1-10.8)

In the figure below, a mass is oscillating on a spring. Which of the following statements are true?

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