Ch. 12 Waves pgs. 436 - 468

Hooke’s Law Periodic motion – a repeated motion Ex. A mass attached to a spring

Hooke’s Law The force always acts toward the equilibrium position – This is called the restoring force At the equilibrium position, velocity reaches a maximum At the maximum displacement, the elastic force and acceleration reach a maximum

Hooke’s Law The direction of the spring force and the acceleration is opposite from the direction of motion The spring force is directly proportional to the displacement of the mass

Hooke’s Law Without friction, the spring would oscillate indefinitely Friction causes the spring to eventually come to rest, this effect is called damping

Hooke’s Law Spring Force units = N Spring Constant units = N/m Displacement units = m

Hooke’s Law Negative sign means direction of the spring force and the direction of the displacement are opposite Spring constant (k) A measure of the stiffness of the spring A large k indicates a stiff spring A small k indicates a soft spring Displacement (x) x = 0 at the equilibrium position

Simple Harmonic Motion Any periodic motion that is the result of a force that is directly proportional to displacement A back and forth motion over the same path The motion of a spring mass system is an example of Simple Harmonic Motion

Simple Harmonic Motion Not all periodic motion over the same path can be considered Simple Harmonic Motion To be Simple Harmonic Motion, the force must obey Hooke’s Law

Elastic Potential Energy A compressed or stretched spring has potential energy The compressed spring, when allowed to expand, can apply a force to an object The potential energy of the spring can be transformed into kinetic energy of the object

If a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium position, what is the spring constant?