Just a and b ### Spring Oscillation ProblemA block with mass \( m \) is connected to a spring and oscillates horizontally on a frictionless table as shown in the diagram below. The position vs. time graph for this mass is also provided. Note that the positive \( x \) direction is defined on the diagram as being to the right.#### Diagram Description- The diagram shows a horizontal spring attached to a block on the right and a wall on the left.- The equilibrium position is marked as \( x = 0 \).- The spring is compressed to the right by a distance \(\Delta x\), indicating the displacement from the equilibrium position.#### Position vs. Time Graph- The graph shows a sinusoidal wave where the position \( x \) (in cm) is plotted against time \( t \) (in s).- The amplitude of the oscillation reaches up to \( \pm 6 \) cm.- The time intervals on the graph are marked, showing one full oscillation cycle, approximately every 4 seconds.#### Questions1. **At what time(s) is the particle at the equilibrium position?**2. **At what time(s) is the particle moving to the right at maximum speed?**3. **At what time(s) is the particle moving to the left at maximum speed?**4. **At what time(s) is the particle instantaneously at rest?**#### Analysis of the Provided Graph- **Equilibrium Position:** The particle crosses the equilibrium position (\( x = 0 \)) at multiple time points within each cycle of oscillation (e.g., around \( t = 1 s \), \( t = 3 s \), \( t = 5 s \), and so on). - **Maximum Speed to the Right:** The particle moves to the right at maximum speed when it passes through the equilibrium position on its way from the negative amplitude to the positive amplitude. This occurs at the points where the slope of the graph is steepest and positive, such as around \( t = 1 s \), \( t = 5 s \), and so forth. - **Maximum Speed to the Left:** The particle moves to the left at maximum speed when it passes through the equilibrium position on its way from the positive amplitude to the negative amplitude. This happens at the points where the slope of the graph is steepest and negative, such as around \( t = 3 s \

Answered: Image /qna-images/answer/de466f73-0013-46b0-b338-91adf3fb76a3.jpg

2. A block with mass m is connected to a spring oscillates horizontally on a frictionless table as shown to the right. Below the figure is the position vs. time graph for this mass. Note that the positive x direction is defined on the diagram as being to the right. a. At what time(s) is the particle at the equilibrium position? X = 0 b. At what time(s) is the particle moving to the right at maximum speed? c. At what time(s) is the particle moving to the left at maximum speed? d. At what time(s) is the particle instantaneously at rest? 6 4 2 x (in cm) 5 Ax 7 +X t (in s)