The photo shows a diagram of a position-time graph for a mass that is oscillating vertically on the end of a spring. The mass is shown superimposed on the graph at three different instants during a single cycle. a. What is the net force and acceleration at position 2? b. What are the directions of the net force and acceleration at position 3? c. At which position, 1, 2, or 3, does the mass have the greatest velocity, and at which position does the mass have the greatest acceleration?

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The photo shows a diagram of a position-time graph for a mass that is oscillating vertically on the end of a spring. The mass is shown superimposed on the graph at three different instants during a single cycle. 

 

a. What is the net force and acceleration at position 2? 

b. What are the directions of the net force and acceleration at position 3?

c. At which position, 1, 2, or 3, does the mass have the greatest velocity, and at which position does the mass have the greatest acceleration? 

**Figure 10-9: Representation of a Simple Harmonic Wave**

**Description:**
Figure 10-9 illustrates a graph of a simple harmonic wave, depicting its displacement over time. The y-axis represents the displacement (amplitude) from the mean position, while the x-axis represents the passage of time.

**Key Components in the Graph:**

1. **Labels on the y-axis:**
   - **A:** Maximum positive amplitude (A)
   - **+x:** Positive displacement
   - **0:** Mean (equilibrium) position
   - **-x:** Negative displacement
   - **-A:** Maximum negative amplitude (-A)

2. **Wave Representation:**
   - The dotted curve in green represents the oscillating wave. It starts from the mean position, moves to the maximum positive amplitude, returns through the mean position to the maximum negative amplitude, and comes back to the mean position, completing one full cycle.

3. **Marked Points:**
   - **Point 1:** Intersection of the wave with the positive displacement (between 0 and +A)
   - **Point 2:** The mean position at the equilibrium
   - **Point 3:** Intersection of the wave with the negative displacement (between 0 and -A)

4. **Time Axis:**
   - The x-axis labeled as "TIME" illustrates the progression of time for one complete oscillation cycle of the wave.

This diagram is crucial for understanding the basic principles of wave motion, particularly in illustrating how the displacement of a particle varies with time in simple harmonic motion.
Transcribed Image Text:**Figure 10-9: Representation of a Simple Harmonic Wave** **Description:** Figure 10-9 illustrates a graph of a simple harmonic wave, depicting its displacement over time. The y-axis represents the displacement (amplitude) from the mean position, while the x-axis represents the passage of time. **Key Components in the Graph:** 1. **Labels on the y-axis:** - **A:** Maximum positive amplitude (A) - **+x:** Positive displacement - **0:** Mean (equilibrium) position - **-x:** Negative displacement - **-A:** Maximum negative amplitude (-A) 2. **Wave Representation:** - The dotted curve in green represents the oscillating wave. It starts from the mean position, moves to the maximum positive amplitude, returns through the mean position to the maximum negative amplitude, and comes back to the mean position, completing one full cycle. 3. **Marked Points:** - **Point 1:** Intersection of the wave with the positive displacement (between 0 and +A) - **Point 2:** The mean position at the equilibrium - **Point 3:** Intersection of the wave with the negative displacement (between 0 and -A) 4. **Time Axis:** - The x-axis labeled as "TIME" illustrates the progression of time for one complete oscillation cycle of the wave. This diagram is crucial for understanding the basic principles of wave motion, particularly in illustrating how the displacement of a particle varies with time in simple harmonic motion.
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