Bell Work: Pendulum IntroBell Work: Pendulum Intro

1. List as many waves as you can. (aim for 10+)

2. List as many examples of pendulums as you can.

Simple Harmonic Motion Simple Harmonic Motion (SHM)(SHM)

Pendulums and WavesPendulums and Waves

Simple Harmonic Motion (SHM)Simple Harmonic Motion (SHM)Motion that repeats regularly without Motion that repeats regularly without changingchanging

Simple Harmonic Motion (SHM)Simple Harmonic Motion (SHM)Original position called equilibrium or Original position called equilibrium or rest positionrest position

A force must be applied to start the A force must be applied to start the motion or to keep the motion goingmotion or to keep the motion going

Resonance:Resonance:– If you add force at the right time, the If you add force at the right time, the

amplitude and energy will stay the same or amplitude and energy will stay the same or increaseincrease

– Ex: push a kid on a swing; instruments are Ex: push a kid on a swing; instruments are shaped to keep certain frequencies of sound shaped to keep certain frequencies of sound inside so that they build up, resonate, and inside so that they build up, resonate, and become louderbecome louder

Simple Harmonic Motion (SHM)Simple Harmonic Motion (SHM)Bouncing spring, pendulums, waves Bouncing spring, pendulums, waves exhibit SHM exhibit SHM

What will determine how a What will determine how a pendulum swings?pendulum swings?

Period (T): time it takes to complete Period (T): time it takes to complete one cycle; unit = sone cycle; unit = s

Length (L): Length (L): – as length increase, as length increase,

period increasesperiod increases– L and T directly L and T directly relatedrelated– Unit = mUnit = m

What will determine how a What will determine how a pendulum swings?pendulum swings?

Gravity (g):Gravity (g):– As gravity increases, period decreasesAs gravity increases, period decreases– g and T are inversely relatedg and T are inversely related– Unit = m/sUnit = m/s22

Frequency (f)Frequency (f)– How often the motion How often the motion occursoccurs– cycles per second; cycles per second;

Unit = Hertz (Hz)Unit = Hertz (Hz)

What will NOT determine how a What will NOT determine how a pendulum swings?pendulum swings?

Mass of the bob Mass of the bob Amplitude (friction can cause slight Amplitude (friction can cause slight

changes)changes)– directly related to how much energy the directly related to how much energy the

pendulum haspendulum has– Not related to period, length, or gravityNot related to period, length, or gravity

Pendulum Equation: Pendulum Equation:

g

LT 2

)4( 2

2

Tg

L LT

g2

24

ExamplesExamplesA. What is the period on Earth of a pendulum with a length of 2.4 m?

B. How long should a pendulum be in order to swing back and forth in 1.6 s?

g

LT 2

8.9

4.22T sT 1.3

)4( 2

2

Tg

L )4(

)6.1)(8.9(2

2

L mL 64.0