Simple Harmonic Motion

Physics

Ms. Shaver

Periodic Motion

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

k: spring

constant

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

• T period (s)

• m mass (kg)

• k spring constant (N/m)

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?

NO. mass and spring constant do not depend on gravity.

Solve for m or k

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=9.8m/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?

Different because the period depends on gravity, which on the moon is 1.62 m/s2

Solving for g or L

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?

NO. There is no m in the equation.

It will increase by the square root of L.

Calculating k from a F vs x Graph

k is the slope of a

F vs x graph

Slope = rise/run= 100 N/5 m= 20 N/m

F = -kxY = mx + b