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## SIMPLE HARMONIC MOTION

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### SIMPLE HARMONIC MOTION STARTER MAKE A LIST OF OBJECTS THAT EXPERIENCE VIBRATIONS: PERIODIC MOTION PERIODIC MOTION: Any motion that repeats itself precisely over equal ... – PowerPoint PPT presentation

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Title: SIMPLE HARMONIC MOTION

1
SIMPLE HARMONIC MOTION
2
STARTER
• MAKE A LIST OF OBJECTS THAT EXPERIENCE VIBRATIONS

3
PERIODIC MOTION
• PERIODIC MOTION Any motion that repeats itself
precisely over equal periods of time.
• If that periodic motion is generated by a linear
restoring force it is SIMPLE HARMONIC MOTION.

4
HOOKEs LAW
• Recall Hookes Law
• F -kx
• x is the amount of extension or compression of a
spring
• Spring constant, k , describes the force
necessary to stretch or compress an individual
spring. Each spring is different.
• the negative sign indicates that the force always
opposes the direction of the stretch, restoring
the object to its rest or equilibrium position

5
Quantities that Describe Periodic Motion
• Period the length of time required to complete
one full cycle of motion
• Frequency the number of cycles in a given time
• Period and frequency are inversely related

6
ENERGY
• ET ½ mv2 ½ kx2
• x is the position
• At the ends of the oscillation the mass stops and
changes direction, so all of the energy is
elastic potential energy
• At equilibrium (x0) the string is not stretched
so all energy is kinetic.

7
VELOCITY
• v vmax v 1- x2/A2
• v is the speed of the mass at any position of its
motion
• x is any position
• A is maximum amplitude
• vmax is the maximum speed occurs at equilibrium
position

8
UNIFORM CIRCULAR MOTION
• The amplitude of SHM is equal to the radius of
Uniform Circular Motion
• Use the UCM equations to describe SHM
• a 4p2A/T2
• vmax 2pA/ T Or T 2pA/ vmax

9
PERIOD and FREQUENCY of mass on spring
• Another arrangement for vmax
• vmax2 k/m A2
• Substituting into UCM equation
• T 2pvm/k
• Equation for frequency
• f 1/2p vk/m

10
PENDULUM
• T 2p v l /g
• l is the length of the pendulum string
• g is acceleration due to gravity
• This equation is valid for the period of a
pendulum for small angles

11
DEFINITION
• Simple Harmonic Motion a periodic vibratory
motion in which the force is directly
proportional to the displacement