A spring-mass system is a physical system consisting of a mass attached to a spring. The spring provides a restoring force that causes the mass to oscillate back and forth around its equilibrium position.
Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. In the spring-mass problem, this means that the force exerted by the spring on the mass is directly proportional to the distance the spring is stretched or compressed from its resting position.
The mass affects the period of oscillation, with a larger mass resulting in a longer period. The spring constant affects the frequency of oscillation, with a larger spring constant resulting in a higher frequency.
Simple harmonic motion occurs when there is no external force acting on the system, resulting in an ideal oscillation with a constant amplitude and frequency. Damped harmonic motion occurs when there is an external force, such as friction, that causes the amplitude of the oscillation to decrease over time.
The equations of motion, such as Newton's second law and Hooke's Law, can be used to set up a system of equations that can be solved to determine the position, velocity, and acceleration of the mass at any given time. These equations can also be used to determine the period, frequency, and amplitude of the oscillation.