Harmonic

Simple Harmonic Motion

By Stacy King

Equilibrium ​position

• ​resting (non moving)

• ​balanced forces

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Oscillating Motion

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External force that alters the equilibrium ​position

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​Forced Vibration

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​the tendency of a vibrating object to lose or to dissipate its energy over time

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Damping

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A force that acts on the oscillating object to restore ​it back to equilibrium

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​​Restoring Force

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Periodic motion

• The motion repeats itself over and over again in cycles.

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What does the graph of position versus time look like?

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​Oscillation

Multiple Choice

Which graph do you think would represent oscillation?

The graph indicates the repeating cycles

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​Graphic Analysis of Oscillation

Multiple Select

MORE THAN 1 is correct.

Which of these would be considered oscillators?

A full cycle is one complete back and forth motion.

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The period is the time it takes to complete one full cycle.

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Period T is measured in seconds.

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​Cycles and Periods

Multiple Choice

What is the period of the Earths rotation?

• 24 hrs

• 48 days

• 24 days

• 48 hrs

Frequency is how many cycles are completed each second.

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Frequency f is measured in hertz, or Hz.​

​Frequency

​Write This Down

Multiple Choice

Javier is on a swing. His feet brush the ground every 3.0 seconds.

What is Javier’s frequency?

• .33

• .17

• 1

• 6

Multiple Choice

Marie has a spring-mass system with a frequency of 4 Hz.  What is the system’s period?

• .25

• 4

• 1

• .17

Oscillations occur in systems with stable equilibrium.

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Stable systems have restoring forces that act to return them to the equilibrium position if they are displaced.

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​Restoring Force

Multiple Choice

What provides the restoring force for a simple pendulum?

• Gravity

• Centripetal

• Friction

​The maximum displacement of the object from equilibrium

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X signifies the displacement variable​ and is measured in meters....

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​Amplitude

Multiple Choice

What is the amplitude of the graph? 

• 1
• 3
• 6
• 9

Equilibrium

• restoring force is zero

​Displacement

• ​restoring force is toward the line of equilibrium

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​Force and Position

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Multiple Choice

.......... is the diatance of the diatance of the oscillating object from yhe equilibrium position at a given instant

• frequency

• time

• period

• displacement

​Kinetic- energy due to motion

Potential-​ energy that is stored

Total mechanical energy​- energy acquired by the objects upon which work is done

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​Some text here about the topic of discussion.

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​Energy and Oscillation Pendulum

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KE = ​1/2 mv²

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KE increases as the object moves toward equilibrium ​

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​Some text here about the topic of discussion.

Calculating Kinetic Energy Pendulum

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Multiple Choice

A body executes simple harmonic motion. The potential energy, the kinetic energy and total energy are measured as a function of displacement x. Which of the following statements is true?

• Kinetic energy is maximum when x = 0

• Total energy is zero, when x = 0

• Kinetic energy is maximum when x is maximum

• Potential energy is maximum when x = 0

PE= mgh​

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​Potential energy is greatest at maximum displacement

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​Some text here about the topic of discussion.

Calculting Potential Energy​ Pendulum

Multiple Choice

Where does a pendulum have maximum potential energy?

• at the bottom of its arc

• at the end of its swing

• as it rises up

• as it falls

Multiple Choice

A pendulum is 0.75 meters long and has a period of 4.17 seconds. The Pendulum is on an unknown planet.  What is the gravity of the Unknown Planet?

• 9.8
• 3.4
• 1.7
• Greater than 9.8

F_spring = -k•x​

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restorative Force is dependent on displacement and the springs ability to stretch (k= the springs constant)

​Motion of Mass on a Spring Hooke's Law

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Multiple Choice

A spring has a spring constant of 450 N/m. How far is the spring compressed if 150 N of force are used?

• 2.2 m

• 3m

• 5.0 m

• 0.3 m

KE = ½•m•v²

​Kinetic Energy

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​PEspring = ½ • k•x²

​elastic potential energy

Kinetic and Potential Energy of a Mass on a Spring

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Multiple Choice

A force of 16 N is required to stretch a spring a distance of 40 cm from its rest position. What force (in Newtons) is required to stretch the same spring …

• 32 N

• not enough info given

• 8 N

• 16 N