Chapter 12 - Vibrations and Waves

Chapter 12 - Vibrations and Waves

Simple Harmonic Motion

Chapter 12 - Vibrations and Waves

Simple Harmonic Motion

Hooke’s Law

http://www.sciencejoywagon.com/physicszone/lessonch/02forces/hookeslaw.htm

In 1678, Robert Hooke discovered the relationship between the distance that a spring is stretched (or compressed) and the amount of force that the spring applies.

Hooke’s Law:

Hooke’s Law:

†

Felastic = -kx

Hooke’s Law:

†

Felastic = -kxWhere:

F is the spring forcek is the spring constant (stiffness)x is the displacement

Effect of Hooke’s Law on a horizontal mass-spring system:

The Force is always in the opposite direction to the displacement.

Since F=ma, the acceleration is also always in the opposite direction to the

displacement.

The spring force always pushes or pulls the mass back to its original equilibrium position.

The spring force always pushes or pulls the mass back to its original equilibrium position.

Therefore, it is sometimes called the restoring force.

The spring force always pushes or pulls the mass back to its original equilibrium position.

Therefore, it is sometimes called the restoring force.

The restoring force is directly proportional to the displacement.

Any periodic motion that is the result of a restoring force that is proportional to the displacement is described by the term simple harmonic motion.

Any periodic motion that is the result of a restoring force that is proportional to the displacement is described by the term simple harmonic motion.

A device that undergoes simple harmonic motion is sometimes called a simple harmonic oscillator or an SHO for short.

A mass hanging on a spring is another example of simple harmonic motion:

Chapter 12 In class practice:

When a 1.00 kg mass is hung on a spring, the spring stretches 3.7 cm from is equilibrium position. Calculate the spring constant.