1. **Stating the problem:** We want to identify and illustrate all the forces acting on a mass $m$ held by a spring, including friction. 2. **Forces involved:** The main forces to consider are: - The **spring force** $\vec{F}_s$, which follows Hooke's Law: $$\vec{F}_s = -k \vec{x}$$ where $k$ is the spring constant and $\vec{x}$ is the displacement vector from equilibrium. - The **gravitational force** $\vec{F}_g$, acting downward: $$\vec{F}_g = m \vec{g}$$ where $\vec{g}$ is the acceleration due to gravity. - The **normal force** $\vec{F}_n$, exerted by the surface supporting the mass, acting perpendicular to the surface. - The **frictional force** $\vec{F}_f$, opposing motion or potential motion, given by: $$\vec{F}_f = -\mu \vec{F}_n$$ where $\mu$ is the coefficient of friction. 3. **Illustration by vectors:** - Draw $\vec{F}_g$ pointing downward. - Draw $\vec{F}_n$ perpendicular and upward from the surface. - Draw $\vec{F}_s$ along the spring, opposite to displacement. - Draw $\vec{F}_f$ parallel to the surface, opposite to the direction of motion or intended motion. 4. **Summary:** These vectors represent all forces acting on the mass in the spring system with friction.