PHYSICAL CONCEPTS Number issues Physical Quantities Force/Friction/Energy/Work, etc. Simple harmonic motion Vibration: Free and Forced Impedance

Scientific Notation number between 1.00 and 9.99 times 10 raised to some power E.G., 1492 becomes x is called the COEFFICIENT

Multiplying numbers in Sci. Not. Multiply coefficients sum powers of 10 E.G. 2.3 x 10 2 x 4x10 3 = (2.3 x 4) x 10 (2+3) = 9.2 x 10 5

Dividing in Sci. Not. Divide Coefficients Subtract Powers of 10 Read More About Exponents in Appendix A

Quantities Come in 2 Flavors: Scalar Quantities –magnitude only Vectorial or Vector Quantities –magnitude AND direction

Scalar Quantities Have magnitude only Examples include Mass, Length, Volume Can be added or subtracted directly

Vector Quantities Have BOTH magnitude and direction Example: Velocity Combining Vectors is more complicated

Basic Units Length Time Mass (Charge)

Other Units may be derived: Area = Length x Length (or L 2 ) Volume = L 3 Speed = Length/Time Acceleration = L/T 2

Force: A push or a pull Force = Acceleration x mass Therefore Force = ML/T 2 MKS force unit is Newton = 1 kg m/s 2 cgs unit is dyne = 1 g cm/s 2

Force and Elasticity Hooke’s Law: Force = (-)spring constant times displacement Stress = force per unit area (aka pressure) Strain = change in length Stress = Elasticity x Strain

Final Comment on Elasticity Compliance is the inverse of Stiffness Greater compliance yields more displacement per unit force Units: L/ML/T 2 (meters/newton, or cm/dyne)

Friction Energy converted into heat when molecules rub against each other. To move an object, the applied force must overcome friction. Effect of Friction is “Resistance”

Friction produces Resistance Resistance = ratio of Force to resulting velocity (R = f/v) measured in Ohms Acoustically, we talk about the influence of friction as DAMPING

Energy & Related Concepts WORK POTENTIAL AND KINETIC ENERGY POWER

WORK Force applied through a distance No motion--no work Work = force x distance = ML/T 2 x L Units JOULE = 1 Newton Meter erg = 1 dyne cm

ENERGY COMES IN 2 FLAVORS Kinetic-- Energy of motion (Inertia can be thought of as the ability to store kinetic energy) Potential--Energy of position (Elasticity --ability to store potential energy)

POWER Rate at which work is done Work/Time Unit Watt = joule/second or 10 7 erg/sec

SIMPLE HARMONIC MOTION Vibration involves interplay of force, inertia, elasticity, and friction Applying a force displaces object Overcoming inertia Traveling away from rest until ?

Simple Harmonic Motion 2 Why does object stop and then move back toward rest? Why doesn’t the object then stop at rest? Where is potential energy the greatest? Where is kinetic energy the greatest?

SHM 3 Why does displacement decrease over time? RESISTANCE -- Energy is lost to HEAT through FRICTION

SHM 4 Amplitude --Displacement Period-- Time taken to complete one cycle Frequency--Number of Cycles per Second Phase--Describing points in the Cycle

A Waveform Shows Amplitude as a Function of Time PEAK PEAK-TO-PEAK

AMPLITUDE MEASURES Instantaneous- amplitude at any given instant Peak Peak to Peak Root Mean Square--A way of getting average amplitude =Square root of Averaged Squared Amplitudes

Period and Frequency Frequency = 1/Period (in seconds) Units of Frequency = cycles per second or HERTZ

PHASE--Each cycle broken up into 360 degrees 0 degrees = 0 displacement and about to head positively 90 degrees = positive maximum 180 degrees=0 disp. About to head negatively 270 degrees= negative maximum

Phase Values Through a Cycle

FREE VIBRATION Pendulum illustration represents FREE VIBRATION Force applied and object allowed to respond Frequency of Free Vibration =Resonant or Natural Freq. --determined by the object’s Mass and Stiffness

FORCED VIBRATION Force is applied back and forth Vibration occurs at the frequency of the applied force Object’s mass and stiffness determine amplitude of vibration

IMPEDANCE The opposition to vibration, or What, other than motion, happens to your applied force? That is what do you have to overcome?

Impedance has 3 components: Resistance: Energy lost to heat through friction Mass Reactance: Energy taken to overcome inertia Stiffness Reactance: Energy taken to overcome restoring force

Impedance and Frequency: Resistance is generally the same across frequency Reactance Components change with frequency

Reactance and Frequency: Mass reactance is greater at high frequencies --it’s harder to get massive objects to vibrate quickly Stiffness reactance is greater at low frequencies --it’s harder to get stiff objects to vibrate slowly

Mass and Stiffness Reactance Resonant Freq.

At Resonant Frequency Mass and Stiffness Reactance Cancel Only opposition to vibration is Resistance In Forced Vibration, you get the most vibratory amplitude for amount of force applied