### Understanding Springs and Oscillations#### Diagram ExplanationThe 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 Analysis1. **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 ProblemA 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.

Answered: Image /qna-images/answer/3d62b37a-a32b-4cc2-84e4-2c54a9d93962.jpg

Answered: 5. Position when spring is unstrained…

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