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Question
**Problem Description: Spring-Mass System Analysis**

A spring with an 8-kg mass and a damping constant of 15 can be stretched 0.5 meters beyond its natural length by a force of 1.5 newtons. Suppose the spring is stretched 1 meter beyond its natural length and then released with zero velocity.

**Objective:**

How can we obtain the expressions for \( c_1 \) and \( c_2 \) in the context of the spring-mass system? 

**Considerations:**

- The system involves calculating the constants for a spring-mass-damping system typically modeled by a second-order differential equation.
- Understanding the initial conditions and how they affect the resulting motion is crucial.
Transcribed Image Text:**Problem Description: Spring-Mass System Analysis** A spring with an 8-kg mass and a damping constant of 15 can be stretched 0.5 meters beyond its natural length by a force of 1.5 newtons. Suppose the spring is stretched 1 meter beyond its natural length and then released with zero velocity. **Objective:** How can we obtain the expressions for \( c_1 \) and \( c_2 \) in the context of the spring-mass system? **Considerations:** - The system involves calculating the constants for a spring-mass-damping system typically modeled by a second-order differential equation. - Understanding the initial conditions and how they affect the resulting motion is crucial.
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