A particle is a point mass with no orientation or rotational inertia. Position is specified using Cartesian coordinates (x,y,z) relative to an origin. Velocity is the derivative of position with respect to time. Acceleration is the second derivative of velocity with respect to time
Spring-mass system consists of mass attached to spring end. Spring constant (k) measures spring stiffness, measured in N/m. Hooke's law states force is proportional to displacement from equilibrium. System can be horizontal or vertical with gravity affecting equilibrium
Mean position of SHM is determined by natural length of spring. Restoring force for displacement x is T = 2π√(m/k). Period depends on both mass and spring constant
Hooke's law states that force is proportional to spring stretch (Fspring = -k•x). Spring constant (k) depends on spring stiffness and is measured in N/m. Spring force acts opposite direction of stretch towards equilibrium position
Derivatives measure function sensitivity to change with respect to input. Trigonometric derivatives are found through differentiation process. Derivatives are used to solve differential equations
Simple harmonic motion occurs in springs and is governed by Hooke's law. Spring force is proportional to the length stretched according to Hooke's law. Spring constant (K) is defined as force per unit of spring extension