Understanding Periodic and Oscillatory Motion

• Motion refers to movement, which can be categorized into various types.
• Periodic motion involves repetitive movements at regular intervals.

Periodic Motion Example

• A weight attached to a string demonstrates periodic motion, swinging back and forth.
• The body tied to the thread will swing left and right repetitively
• This type of motion, where movement repeats, is called periodic motion.
• Periodic motion is motion which is repeated in equal durations of time intervals.
• Motion types include oscillatory motion (like a pendulum) and wave motion.

Oscillatory Motion

• Oscillatory motion involves an object moving back and forth around a central point.
• In oscillatory motion, a body swings around a resting position.
• Rest point is the position where the moving object starts.
• Maximum displacement refers to the farthest point the object reaches in its motion.
• An object moves from the starting position (rest point) towards the right side.
• Each side is maximum displacement because the object cannot go any further
• The object will then return to the starting position.
• Motion continues past the starting position to the opposite (left) side.
• The object will return to the starting position and the process will keep repeating
• Time duration on the right side is the same as on the left side.
• The body moves around the rest position.
• Oscillatory motion is always around a rest position.

Kinetic Energy

• Due to the motion Kinetic energy exist
• Kinetic Energy = Half x Mass x Velocity Squared
• Faster and heavier objects have more kinetic energy.
• The higher either variable goes the more kinetic energy there is

Oscillatory Motion Example 2

• Instead of moving from right to left the object will now move up and down
• The object will move around a point of origin
• This point is called the rest position
• The rest position is where the object starts
• A 100g weight is suspended and allowed to move freely
• The weight rises and falls, around the rest position
• When furthest the body will slow down
• The object slows down as it moves away from the original point.
• The object speeds up as it comes back towards rest
• As the object moves back towards the rest position it starts to speed up significantly

Examples of motion

• Pendulums, guitars, and swings are examples of oscillatory motion
• The movement of a swing demonstrates repetitive motion.

Graphical Representation of Oscillating Motion

• The oscillations have to be drawn on paper
• A tool will draw the motion on a graph while it happen
• The device draws the motion as the object move ups and down
• The graph will show the objects relation to the rest position
• The object is static, than begins to move forward
• The object returns to the original position after a while
• The object moves to the left side, and than returns
• The graph of this motion is called "simple harmonic motion".
• A graph can show the motion of an object which is repetitive harmonic
• The up and down motion can be used to show how the object correlates to the rest or original location

Harmonic Motion

• Starting in the positive direction, an object can travel from point A to point C
• As the body goes towards the top it slows down and stops, and immediately comes back down
• Since the object stopped and now is going back down it is completing the motion from C to A.
• When the object is back in the rest position, does the body stop?
• No! The body will continues from point A to point B.
• The object is going in another direction and will stop at B
• B is the maximum displacement, like with point C
• Once the body gets to B, it will no longer stay, but come back from B to A
• The object is now back to A and the moment has been completed
• There is always four stages of movement
• Oscillatory motion involves an object at a central point, with movement on either side.

Four stages

• The device starts in its resting position
• the object begins to move towards point B
• The object has left its resting position, and now moving back again
• The same motions are preformed on the opposite side
• In simple words
  • One motion
  • Half oscillation
  • Three quarter oscillation
  • Return to starting position

Amplitude

• A complete "oscillation" always includes four amplitude
• It is the distance to the highest point
• An object can be traveling to its lowing point, and the space would still be aptitude
• Always remember that distance is measured in m (meters).

Periodic Time

• Periodic time is the length of time taken for the object to make one complete "oscillation”
• One complete "oscillation" is when there are the four amplitudes are finished and restarts
• Periodic time is measured in seconds

Frequency

• If and object repeatedly moves back and forth it is called "Oscillation"
• How many "Oscillations" can it make in a second?
• A second by definition must be only taking 1 second to mark
• The number of "Oscillations" an object makes in a second is called "Frequency”.
• Frequency is how many oscillations per 1 second
• "Frequency" unit of measurement is called Hertz
• "Frequency" and periodic time are different units

Laws

• Periodic time = Time / Number of complete oscillation
• Frequency = Number / Time
• Some common transformations you will need to know when frequency transformations -Mega hertz -Kilo hertz -Giga hertz

Relation between Frequency and Periodic Time

• When you calculate the frequency of periodic time you may not need to use either periodic time or frequency rolls
• A shorter form can involve frequency = 1 / to periodic time
• and periodic time = 1/ to frequency
• The relationship between frequency and periotic time is the complete opposite.