Simple Harmonic Motion Physics Mrs. Coyle

Periodic Motion

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Simple Harmonic Motion: 1.Is a periodic motion that repeats at constant frequency. 2.Has a restoring force that acts to restore the oscillator to equilibrium. F=-kx Hooke’s Law x: displacement from equilibrium

Characteristic Quantities of Simple Harmonic Motion Displacement: distance from equilibrium. Amplitude: maximum displacement

Characteristic Quantities of Simple Harmonic Motion Frequency: oscillations per unit time –Unit: 1/sec =Hertz Period: time to complete one oscillation –Unit: sec f=1/T T=1/f

Simple Harmonic Motion Velocity: –maximum as it passes through equilibrium –zero as it passes through the extreme positions in its oscillation. Acceleration: a=F/m = -kx/m -maximum at extreme points -zero at equilibrium

Mass on a Spring Applet:

Position vs Time Graph of Mass on Spring (Sine Curve) a)What is the amplitude? b)What is the period? c) What total distance does the particle travel in one period? x

Period of A Spring Mass Oscillator ____ T=2  √m/k m mass k spring constant

Problem Calculate the period of a mass of 5kg on a spring that has a spring constant of 20N/m. Answer: 3s

Question If you had a spring-mass system on the moon, would the period be the same or different than that of this system on the earth?

Harmonic Motion of a Pendulum Applets: ons6e/index.htm?newwindow=true ons6e/index.htm?newwindow=true L

Harmonic Motion of a Pendulum ons6e/index.htm?newwindow=truehttp://www3.interscience.wiley.com:8100/legacy/college/halliday/ /simulati ons6e/index.htm?newwindow=true Period ___ T=2  √L/g g=10m/s 2 L=length of string L

Problem Calculate the Period of a pendulum of length 0.75 m. Answer: 1.7s

Question If you had a pendulum on the moon would its period be the same or different compared to the same pendulum on the earth?

Questions Does the period of a pendulum depend on the mass of the bob? If you increase the length of the pendulum string, what happens to the period?

Calculating k from a F vs x Graph k is the slope of a F vs x graph