Simple Harmonic Motion Periodic Motion When a vibration

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 200 kg) steps into their 1200 kg 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 100 kg 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 15 cm 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)