Periodic motion

Periodic motion

1. Mass on a spring

   • periodic motion: motions that repeat in a in a regular cycle. period is the time needed for an object to repeat one complete cycle of the motion. the amplitude of the motion is the maximum distance the object moves from the equilibrium position. Simple harmonic motion: any system in which the force acting to restore an object to its equilibrium position is directly proportional to the displacement of the object.

2. Hooke's law

   • a force directly proportional to the distance stretched.
     • Formula: F= -kx
       • K is spring constant, it depends on the stiffness and other properties of the spring. x is the distance the spring is stretched.
       • a negative sign indicates that the force is in the direction opposite the stretch or compression direction.
   • Not all springs obey Hooke's Law. rubber bands don't. The ones that do are called elastic springs. the law is applied only over a limited range of distances. if the spring is stretched to far, the spring may exceed its elastic limit.
   • Potential energy: when a spring is stretched, energy is transferred to the spring, giving it elastic potential energy.
     • PEspring= 1/2(kx^2)

3. Pendulums

   • a simple pendulum consists of a massive object that swings back and forth. the string exerts a tension force and gravity exerts a force on the bob.
     • the period depends only on the length of the pendulum and the gravitational field, not on the mass of the bob.

4. Resonance

   • resonance occurs when forces are applied to a vibrating or oscillating object at time intervals equal to the period of oscillation.
   • causes a larger and larger displacement as energy is added in small increments.