5. Position when spring is unstrained www Xf xo In the figure above the mass attached to the spring is 0.2 kg. The spring's constant is 40 N/m. The mass is stretched to a position of 0.3 m and released. The final position is 0.1m. 1. Find the change in potential energy of the system. 2. What is the work done by the spring? A spring whose spring constant is 120 N/m has a 0.1 kg block attached to it. The spring and mass sit on a horizontal frictionless surface. The block is pulled 0.2 m and released. 1. Find the frequency of the oscillations 2. Find the period of the oscillations 3. Find the angular frequency of the oscillations (0) 4. Find the amplitude of the oscillations 5. Find the maximum velocity of the block 6. Find the maximum acceleration of the block 7. Write expressions for the displacement, velocity and acceleration as functions of time.
5. Position when spring is unstrained www Xf xo In the figure above the mass attached to the spring is 0.2 kg. The spring's constant is 40 N/m. The mass is stretched to a position of 0.3 m and released. The final position is 0.1m. 1. Find the change in potential energy of the system. 2. What is the work done by the spring? A spring whose spring constant is 120 N/m has a 0.1 kg block attached to it. The spring and mass sit on a horizontal frictionless surface. The block is pulled 0.2 m and released. 1. Find the frequency of the oscillations 2. Find the period of the oscillations 3. Find the angular frequency of the oscillations (0) 4. Find the amplitude of the oscillations 5. Find the maximum velocity of the block 6. Find the maximum acceleration of the block 7. Write expressions for the displacement, velocity and acceleration as functions of time.
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Transcribed Image Text:### Understanding Springs and Oscillations
#### Diagram Explanation
The image depicts a horizontal spring-mass system:
- **Mass**: 0.2 kg
- **Spring Constant (k)**: 40 N/m
- **Initial Stretch**: 0.3 m
- **Final Position**: 0.1 m
- **Unstressed Position**: Marked as \( x_0 \)
#### Questions for Analysis
1. **Change in Potential Energy**
- Determine how much the potential energy of the system changes as the mass moves from the initial to the final position.
2. **Work Done by the Spring**
- Calculate the work done by the spring on the mass during its motion.
#### Additional Spring-Mass System Problem
A different system is described:
- **Spring Constant**: 120 N/m
- **Mass**: 0.1 kg
- **Initial Stretch**: 0.2 m
- **Surface**: Frictionless
**Tasks:**
1. **Frequency of Oscillations**
- Calculate the frequency at which the system oscillates.
2. **Period of Oscillations**
- Determine the period of the oscillations.
3. **Angular Frequency (ω)**
- Find the angular frequency of the oscillations.
4. **Amplitude of the Oscillations**
- Calculate the maximum displacement from the equilibrium position.
5. **Maximum Velocity of the Block**
- Determine the highest speed the block reaches during oscillations.
6. **Maximum Acceleration of the Block**
- Find the greatest acceleration experienced by the block.
7. **Equations of Motion**
- Develop expressions for displacement, velocity, and acceleration as functions of time for the oscillating block.
Use these analyses to understand the behavior of spring-mass systems and their applications in physics.
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