Transcript Simple Harmonic Motion

Simple Harmonic Motion
Periodic Motion
• When a vibration or oscillation repeats
itself over the same time period
Oscillating Spring System
• Equilibrium positionwhere spring exerts
no force on the mass
(m)
• Natural state
Oscillating Spring System
• Spring stretched
• Exerts a force to
move it back to
equilibrium
Oscillating Spring System
• Spring compressed
• Force exerted pushing
it back to equilibrium
Restoring Force (F)
• Force exerted when away from equilibrium
- pulls it back to equilibrium
• Directly proportional to the displacement
(x)
F = - kx
• k – spring constant
• Greater the value of k the more force is
needed to stretch spring - stiffer
• F is not constant, depends on x
• F = ma
• Therefore acceleration is not constant,
depends on x
Question
• At what position(s) is the acceleration the
greatest?
• Where is it the least?
• Where is velocity greatest? And least?
Other Definitions
• Amplitude (A) – point of greatest
displacement
• Cycle – complete oscillation
• Period (T) – time for one complete
oscillation
• Frequency (f) – cycles per second
T = 1/f
Example
• When a family of four people (total mass
200kg) steps into their 1200kg car, the
springs compress 3.0 cm. A) What is the
car’s spring constant? B) How far will the
car lower if loaded with 100kg of luggage
as well?
Example
• A .10 kg object is suspended from a spring
with a spring constant of 10 N/m. The
object is pulled 15cm from its equilibrium
position and released, what is its maximum
acceleration and when does it experience
this?
Simple Harmonic Motion
(SHM)
• Any vibrating system where the restoring
force is directly proportional to the
negative displacement
• Any object exhibiting this is called a
simple harmonic oscillator (SHO)