Simple Harmonic Motion Vibrations and Waves Simple Harmonic Motion

Hooke’s Law Periodic motion – repeated motion Usually back and forth over the same path at regular time intervals Equilibrium position – the point in the motion where the net force on an object is zero At the equilibrium point, velocity reaches a maximum At maximum displacement. Spring force and acceleration reach a maximum Velocity is zero

Hooke’s Law

Hooke’s Law Simple harmonic motion – vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium Hooke’s Law = spring force = -(spring constant * displacement) Felastic = -kx k is measured in N/m Felastic is measured in N

Hooke’s Law Remember that stretched or compressed objects have elastic potential energy This causes the object to repeat its motion

The Simple Pendulum A simple pendulum consists of a bob and string The bob – the part of the pendulum that swings back and forth We disregard the mass of the string, air resistance, and friction The restoring force of a pendulum is a component of the bob’s weight The same conclusions that we drew with springs about force, displacement, and velocity are true for pendula as well, with small angles

The Simple Pendulum

The Simple Pendulum At the equilibrium point, velocity reaches a maximum At maximum displacement, force and acceleration reach a maximum Velocity is zero Gravitational potential energy increases as a pendulum’s displacement increases Kinetic energy increases as the pendulum nears the equilibrium point

The Simple Pendulum

The Simple Pendulum