A spring with \(k=200\,\mathrm{N\,m^{-1}}\) is compressed by \(0.10\,\mathrm{m}\). Find \(U_s\).

A spring has \(k=50\,\mathrm{N\,m^{-1}}\) and extension \(0.20\,\mathrm{m}\). Find the spring force magnitude.

If a spring is compressed by \(-x\) instead of stretched by \(+x\), how does \(U_s\) compare?

What are the SI units of the spring constant \(k\)?

A \(0.50\,\mathrm{kg}\) block is launched by a \(100\,\mathrm{N\,m^{-1}}\) spring compressed \(0.20\,\mathrm{m}\). Find launch speed on a frictionless surface.

A spring stores \(8\,\mathrm{J}\) when compressed by \(0.20\,\mathrm{m}\). Find \(k\).

A spring with \(k=300\,\mathrm{N\,m^{-1}}\) is stretched from \(0.10\,\mathrm{m}\) to \(0.30\,\mathrm{m}\). Find \(\Delta U_s\).

A \(2\,\mathrm{kg}\) block moving at \(3\,\mathrm{m\,s^{-1}}\) compresses a spring with \(k=400\,\mathrm{N\,m^{-1}}\). Find maximum compression.

A vertical spring with \(k=500\,\mathrm{N\,m^{-1}}\) is compressed \(0.12\,\mathrm{m}\) and launches a \(0.30\,\mathrm{kg}\) mass upward. Find the height gained after the spring returns to natural length.

A block starts at rest against a compressed spring on a rough horizontal surface. The spring has \(k=250\,\mathrm{N\,m^{-1}}\), compression \(0.30\,\mathrm{m}\), and friction does \(4\,\mathrm{J}\) of negative work before the block leaves the spring. Find the exit speed for \(m=1.0\,\mathrm{kg}\).

A block of mass \(m\) starts from rest a vertical height \(h\) above the point where it first touches an uncompressed spring mounted along a frictionless incline of angle \(\theta\). During compression it moves an additional distance \(x\) down the incline. Derive the maximum compression \(x\).

A mass \(m\) hangs from a vertical spring of constant \(k\) and is released from rest at the spring's natural length. Taking \(y\) downward from the natural length, find the equilibrium position, the maximum downward displacement, and the shifted-coordinate form that explains the motion.