Spring
A mass is suspended by a spring. The forces acting on the mass are due to gravity and the distension of the spring.Pull the mass down, let it go, and it will oscillate up and down.
The independent variable is time.
The resting length of the spring is the length at which it produces no force. The force produced by the spring is the product of its stiffness and displacement from resting length.
The mass's upward acceleration is equal to spring force divided by mass minus the acceleration of gravity.
The velocity of the mass is the integral over time of its acceleration. The position of the mass is the integral over time of its velocity.
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