A mass is attached to the end of a horizontal spring that oscillates frictionlessly. At which point in the motion of the mass does it have zero velocity? O At x = 0, the equilibrium point At x = ±A/2, midway between equilibrium and the endpoints At x = ±A, the endpoints of its motion O Nowhere, the velocity is always positive

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Chapter1: Units, Trigonometry. And Vectors
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### Simple Harmonic Motion and Velocity

In this example, we explore the motion of a mass attached to the end of a horizontal spring that oscillates without any friction.

**Question:**
A mass is attached to the end of a horizontal spring that oscillates frictionlessly. At which point in the motion of the mass does it have zero velocity?

**Options:**

1. **○ At \( x = 0 \), the equilibrium point**
    - The point where the spring is neither compressed nor stretched and the velocity is maximum, not zero. 

2. **○ At \( x = \pm A/2 \), midway between equilibrium and the endpoints**
    - The velocity is not zero at these points. At these positions, the mass is in motion either towards or away from the equilibrium position.

3. **○ At \( x = \pm A \), the endpoints of its motion**
    - Correct! The velocity of the mass becomes zero at the endpoints of its oscillation. This is because these points are where the direction of motion reverses.

4. **○ Nowhere, the velocity is always positive**
    - This is incorrect because the mass will come to a stop momentarily at the endpoints, implying a zero velocity at those points.

**Explanation:**

The point where the velocity of an oscillating mass is zero is at the endpoints of its motion (\( x = \pm A \)). At these endpoints, the mass momentarily comes to a halt before changing direction. Thus, the correct answer is:

**○ At \( x = \pm A \), the endpoints of its motion**
Transcribed Image Text:### Simple Harmonic Motion and Velocity In this example, we explore the motion of a mass attached to the end of a horizontal spring that oscillates without any friction. **Question:** A mass is attached to the end of a horizontal spring that oscillates frictionlessly. At which point in the motion of the mass does it have zero velocity? **Options:** 1. **○ At \( x = 0 \), the equilibrium point** - The point where the spring is neither compressed nor stretched and the velocity is maximum, not zero. 2. **○ At \( x = \pm A/2 \), midway between equilibrium and the endpoints** - The velocity is not zero at these points. At these positions, the mass is in motion either towards or away from the equilibrium position. 3. **○ At \( x = \pm A \), the endpoints of its motion** - Correct! The velocity of the mass becomes zero at the endpoints of its oscillation. This is because these points are where the direction of motion reverses. 4. **○ Nowhere, the velocity is always positive** - This is incorrect because the mass will come to a stop momentarily at the endpoints, implying a zero velocity at those points. **Explanation:** The point where the velocity of an oscillating mass is zero is at the endpoints of its motion (\( x = \pm A \)). At these endpoints, the mass momentarily comes to a halt before changing direction. Thus, the correct answer is: **○ At \( x = \pm A \), the endpoints of its motion**
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