Spring

A spring with constant $k$ is at the top of a frictionless incline of angle $\theta$. The lower end of the incline is a distance $D$ from the spring's relaxed position. A canister of mass $m$ is pushed against the spring until it is compressed by a distance $x$ and released from rest.

A block of mass $m$ slides from rest a distance $d$ down a frictionless incline at an angle $\theta$ to the horizontal. It then runs into a spring of spring constant $k$. When the block momentarily stops, it has compressed the spring by a distance $x$.

A spring-loaded gun is mounted horizontally on a table. A child tries to hit a small target box on the floor, located a horizontal distance $D$ from the edge of the table. In the first attempt, the spring is compressed by a distance $x_1$, and the marble falls short of the center of the box by a distance $S_1$. Assume no friction.

A block C of mass $m = 2$ kg is placed on a smooth inclined plane with an angle of inclination $\alpha = 30^\circ$. It is attached to a light spring with an unstretched length of $l_0 = 0.2$ m. The other end of the spring is fixed at the top of the incline. When the system is at rest, the spring stretches to a length of $l_1 = 0.25$ m. The entire system (incline and block) rotates about a vertical axis AB as shown. (Use $g = 9.8$ m/s²)

A force of $F = 120$ N is required to compress a spring by $x_1 = 4$ cm.

A spring with a natural length of $20$ cm and a spring constant of $k = 1000$ N/m is stretched.

A light spring with a spring constant $k = 360$ N/m has one end fixed. The other end is attached to a small ball of mass $m = 100$ g, which is placed on a smooth horizontal surface. The ball is pulled from its equilibrium position to a displacement of $x_1 = 10$ cm and then released from rest.

A 2.0 kg block on a horizontal surface is pushed against a light horizontal spring (spring constant 200 N/m), compressing it by 15 cm. The block is then released from rest. After leaving the spring (at its equilibrium position), the block slides 60 cm before coming to a stop.

A block of mass $m$ is dropped onto a relaxed vertical spring with a spring constant $k$. The block attaches to the spring and compresses it by a maximum distance $x_m$ before momentarily stopping. Let $v_i$ be the speed of the block just before it hits the spring. Friction is negligible.

A block of mass $m$ is placed against a spring with spring constant $k$ on a frictionless incline with an angle of inclination $\theta$. The block is not attached to the spring. The spring is initially compressed by a distance $x$ from its equilibrium position. The block is then released from rest.