Simple Harmonic Motion

Physics

Mrs. Coyle

Periodic Motion

Periodic Motion

http://www.cleonis.nl/physics/inertosc_img/harmonic_oscillation.gif

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 Lawx: 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 SpringApplet:

http://www.walter-fendt.de/ph14e/springpendulum.htm

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:

• http://www.walter-fendt.de/ph14e/pendulum.htm •

http://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/simulations6e/index.htm?newwindow=true

L

Harmonic Motion of a Pendulum• http://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/

simulations6e/index.htm?newwindow=true

• Period ___ T=2√L/g

g=10m/s2

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