Question
A pendulum makes a complete swing as shown in the picture above. Describe the motion of the pendulum at points A, B, and C. Be sure to use the words maximum velocity, minimum velocity, maximum displacement, minimum displacement, maximum acceleration, minimum acceleration, equilibrium, and restoring force where appropriate.
Answers
GPT-4o mini
The motion of a pendulum can be described at various points during its swing. Let's analyze points A, B, and C based on their positions in the swing of the pendulum:
1. **Point A (Highest Point on One Side)**:
- At point A, the pendulum is at its **maximum displacement** from the equilibrium position. This is the point where the pendulum will change direction.
- The **velocity** of the pendulum is at its **minimum** (essentially zero) as it pauses momentarily before swinging back down.
- The **acceleration** of the pendulum is at its **maximum** because the restoring force (gravity acting on the pendulum) is greatest at this height.
- Here, the restoring force is directed towards the equilibrium position, attempting to bring the pendulum back to its lowest point.
2. **Point B (Lowest Point in the Swing)**:
- At point B, the pendulum is at its **minimum displacement** from the equilibrium position, which is the point of maximum kinetic energy and velocity.
- The **velocity** is at its **maximum** at this point, as the pendulum swings through the equilibrium position.
- The **acceleration** here is at its **minimum**, as the restoring force is the weakest when the pendulum is at the lowest point; this is because the net force acting on the pendulum is also minimal at this position before it starts to rise again.
3. **Point C (Highest Point on the Opposite Side)**:
- At point C, similar to point A, the pendulum is again at its **maximum displacement**, but on the opposite side of the swing.
- The **velocity** is at its **minimum** (essentially zero) as it reaches the peak before reversing direction again.
- The **acceleration** is at its **maximum** here, directed towards the equilibrium position due to the restoring force of gravity.
- The restoring force is significant because it acts to pull the pendulum back down toward the center.
In summary, while the pendulum oscillates between points A (maximum displacement, minimum velocity, maximum acceleration), point B (minimum displacement, maximum velocity, minimum acceleration), and point C (maximum displacement, minimum velocity, maximum acceleration), the interplay of velocity, displacement, acceleration, and restoring force creates the characteristic motion of the pendulum.
1. **Point A (Highest Point on One Side)**:
- At point A, the pendulum is at its **maximum displacement** from the equilibrium position. This is the point where the pendulum will change direction.
- The **velocity** of the pendulum is at its **minimum** (essentially zero) as it pauses momentarily before swinging back down.
- The **acceleration** of the pendulum is at its **maximum** because the restoring force (gravity acting on the pendulum) is greatest at this height.
- Here, the restoring force is directed towards the equilibrium position, attempting to bring the pendulum back to its lowest point.
2. **Point B (Lowest Point in the Swing)**:
- At point B, the pendulum is at its **minimum displacement** from the equilibrium position, which is the point of maximum kinetic energy and velocity.
- The **velocity** is at its **maximum** at this point, as the pendulum swings through the equilibrium position.
- The **acceleration** here is at its **minimum**, as the restoring force is the weakest when the pendulum is at the lowest point; this is because the net force acting on the pendulum is also minimal at this position before it starts to rise again.
3. **Point C (Highest Point on the Opposite Side)**:
- At point C, similar to point A, the pendulum is again at its **maximum displacement**, but on the opposite side of the swing.
- The **velocity** is at its **minimum** (essentially zero) as it reaches the peak before reversing direction again.
- The **acceleration** is at its **maximum** here, directed towards the equilibrium position due to the restoring force of gravity.
- The restoring force is significant because it acts to pull the pendulum back down toward the center.
In summary, while the pendulum oscillates between points A (maximum displacement, minimum velocity, maximum acceleration), point B (minimum displacement, maximum velocity, minimum acceleration), and point C (maximum displacement, minimum velocity, maximum acceleration), the interplay of velocity, displacement, acceleration, and restoring force creates the characteristic motion of the pendulum.