· When a spring is stretched, it experiences a positive force and displacement.

· When it is compressed, the force and displacement are negative.

· The spring constant is the amount of force needed to stretch the spring a given distance.

· A spring that has a spring constant that is equal to the applied force divided by the displacement is said to be an ideal spring.

· The shorter the spring, the greater the spring constant.

· When a force is applied to a spring, the spring exerts an equal and oppositely directed force back. This is called a reaction force, or a restoring force.

· Simple harmonic motion is the oscillatory motion that occurs when a restoring force acts on an object.

· The amplitude A of the motion is the maximum distance that the object moves away from its equilibrium position.

· The period T is the time it takes for the object to complete one cycle of motion, while the frequency f is the number of cycles per second that occur.

· The greater the angular speed, the shorter the time it takes for one revolution.

· In simple harmonic motion, the velocity is not constant, so therefore, there must be acceleration, which does not remain constant either.

· Elastic potential energy is the energy that a spring has by virtue of being stretched or compressed.

· For an ideal spring that has a constant k, and is stretched or compressed by an amount x relative to its unrestrained length, the elastic potential energy is PE_{elastic = ½ kx^2.}

· The total mechanical energy of a spring system is the sum of its translational and rotational kinetic energies, gravitational potential energy, and elastic potential energy.

· If external forces such as friction do no net work on the system, the total mechanical energy of the system is conserved.

· A simple pendulum consists of a particle of mass m attached to a frictionless pivot P by a cable of length L, and negligible mass.

· The force of gravity is responsible for the pendulums back and forth movements.

· The rotation speeds up as the particle approaches the lowest point on the arc, and slows down on the upward part of the spring.

· The tension in the cable produces no torque because it points directly at the pivot and has no lever arm. The lever arm is the perpendicular distance between the line of action of mg and the pivot P.

· A physical pendulum consists of a rigid object with moment of inertia I, and mass m, suspended from a frictionless pivot.

· In Damped harmonic motion, energy-dissolving mechanisms such as friction are always present.

· Critical damping is the minimum degree of damping that eliminates any oscillations in the motion as the object returns to its equilibrium system.

· When the damping exceeds the critical value, the object is said to be over-damped.

· When the damping is less than the critical value, the object is said to be under-damped.