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
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
![### 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**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fc0f41c-1d8b-41a4-aee9-3a82e03a5afd%2F0597d475-6c12-4803-9def-d7be61dc855c%2Fd928lpr.png&w=3840&q=75)
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