Simple Harmonic Motion

Springs The force from a spring depends on the mass The greater the mass, The greater the spring force

Hooke’s law F = - k x F is force (N) k is the spring constant (N/m) “The magnitude of the force exerted by a spring is equal to the spring constant times the distance the spring is stretched or compressed from its equilibrium position” F = - k x F is force (N) k is the spring constant (N/m) x is the distance from equilibrium (m) Why “-”? Because the force is in the opposite direction that the spring is being stretched!

F = -kx2 PEsp= ½kx2 Warm up A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from its end. Determine the spring constant How much elastic potential energy does the spring have when it is stretched this far?

Periodic Motion Motion that repeats in a regular cycle Mass on a spring Vibrating guitar string Tree swaying in the wind Equilibrium Position- where the net force on the object is zero All other positions, there is a force working to bring the object back to equilibrium

Periodic Motion Period (T) – amount of time needed for an object to complete one cycle of motion Amplitude – the maximum distance the object is from the equilibrium point

Simple harmonic motion When a force acting to restore an object is directly proportional to the displacement of the object Ex: The force exerted by a spring is proportional to how far the spring is stretched

Hooke’s law F = - k x The force from the spring changes depending on the displacement PEspring = ½kx2 KE + PE = ME

Mass on a spring interactive

Mass on a spring

Mass on a spring and energy Where is there maximum potential energy? Where is there maximum kinetic energy? Max Potential: top and bottom of range of motion Max Kinetic: at equilibrium position

Energy distribution through range of motion (Page 384 of your textbook