Simple Harmonic Motion A.S – Due Tuesday, March 24 WebAssign Due Tuesday, March 24 Quiz on Tuesday, March 24 Warm-up (March 16): Predict what will happen to the period of an oscillating mass if the amplitude is increased? If the mass is increased?

Hooke’s Law The force applied to a spring in order to extend or compress it is proportional to the amount of displacement of the spring from its rest position. The spring force will be equal and opposite to the applied force, as it is a tension that is a reaction force to the applied force

Elastic Limit Once a spring has reached its elastic limit, it will not return to its original length. Hooke’s Law only applies if a spring will return to its original position (length) By definition: Elastic Limit is the maximum range of extension(or compression) for which Hooke’s law is satisfied.

SHM for a Mass on a Horizontal Spring Rest Position: the position of the mass when it is experiencing no net force Restoring Force: the force the spring applies to the mass in order to pull it back to the rest position. ◦ The strength of the force depends on the displacement of the mass and the spring constant of the spring. Displacement: The change in position of the mass relative to its rest position ◦ The positive direction must be defined and kept constant for a system.

Conditions for SHM:

Angular Frequency (  ) Frequency, in general (linear frequency), is simply a count of how many times the mass reaches a set point per second. ◦ For an oscillation: The number of times per second an oscillating mass completes one full cycle (one full oscillation) ◦ In one oscillation, how does the motion compare to circular motion? Angular Frequency puts the count found in linear Frequency in terms of the amount of radians the mass has covered per second.

Angular Frequency

Quick Sample:

Back to our spring:

SHM Defining Equation

Fundamental Vocabulary:

Exploration lab: You’ll be exploring the behavior of an object in simple harmonic motion, and will be observing the effect of a variety of variables on the period of the oscillations you see. All observations will be done in your lab book, and you’ll be printing a few graphs and taping them in your books as well.