Force Analysis of Simple Harmonic Motion

Simple Harmonic Motion

By Stacy King

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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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

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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

The graph indicates the repeating cycles

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​Graphic Analysis of Oscillation

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

Frequency is how many cycles are completed each second.

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Frequency f is measured in hertz, or Hz.​

​Frequency

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​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

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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Force Analysis of Simple Harmonic Motion

By Stacy King

The restoring force causes the vibrating object to slow down as it moves away from the equilibrium position and to speed up as it approaches the equilibrium position​

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​Restoring Force of Pendulum

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Gravity- pulling down

​Tension- acting upward

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​Forces acting on the pendulum

​D- zero position

• ​left is negative direction

• right is positive​ direction

• ​velocity is greatest

G and A - greatest displacement

• ​velocity is the least

  • ​due to the restoring force

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Sinusoidal Nature of Pendulums​

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​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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Multiple Choice

Stored energy is referred to as

• kinetic

• potential

• total mechanical energy

• mass in motion

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

​The sum of the two forms of energy

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PE + KE= total mechanical energy​

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​Total Mechanical Energy

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Multiple Choice

If at point D the pendulum is 4 J of potential energy then the KE is

• 0

• -4

• -2

• 2

​ the time it takes for a vibrating object to complete its cycle

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What variables affect the period of a pendulum?

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​Period of a pendulum

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The most important Variable that affects the period is the length of the pendulum from the axis point​

Pendulum Period

Multiple Choice

Which would have the highest frequency?

object A mass=400kg and length 2m

Object B mass= 600kg and length .25m

• A

• B

• not enough information

• they would be the same

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

Fspring = -k•x​​

​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

the time for a vibrating object to make one complete cycle of vibration​

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​The variables that affect the period of the mass on a spring

• k the spring constant

• mass ​

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Period of Mass on a Spring

Multiple Choice

Which would have a higher frequency?

Object A mass= 200g with a k= 600Nm

Object B mass=200g with a k=400Nm

• object A

• object B

• not enough information

• they would be the same

Multiple Choice

Which would have a higher frequency?

Object A mass= 300g with a k= 400Nm

Object B mass=200g with a k=400Nm

• object A

• object B

• not enough information

• they would be the same