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Any motion that regularly repeats is referred to as _______ or ________ motion. Ideal type of oscillatory motion is referred to as _______ ________ _______ (___). This type of motion oscillates about an _________ position
- periodic or harmonic motion
- simple harmonic motion (SHM)
- equilibrium
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Objects or systems of objects that undergo oscillatory motion are called ________.
State 3 common examples:
This type of motion can be characterized by its _______ or _______
- oscillators
- Common examples:
- 1) Object undergoing uniform circular motion
- 2) A mass oscillating on a spring
- 3) A pendulum
- period or frequency
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Define the equilibrium position.
For a horizontal spring mass system, equilibrium is at the ______ ______ _____. For a vertical spring mass system, the weight of the mass will stretch the spring so equilibrium is no longer at its ______ length. The new equilibrium position is when the upward force of spring exactly balances the ______ of the mass
- Equilibrium position: A point at which the net force on the particle is zero (ΣF = 0).
- spring's natural length
- resting length
- weight
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For a simple pendulum, the equilibrium position is in a _______ position. A reference configuration for x = ____ is at equilibrium position. This enables us to "ignore ______" for vertical spring mass systems
- vertical
- 0
- "ignore gravity"
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Explain how the force exerted by the spring will act in each of these scenarios
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Draw a period versus time graph for each of the following scenarios:
The oscillation takes place around an equilibrium position (Label the equilibrium position)
The motion is periodic One cycle takes time T (Describe and Label the period)
The oscillation is sinusoidal
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Define Period
Period (T): T, the time interval required for the particle to go through one full cycle or the time it takes the particle to make one revolution or a round trip
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Define Round trip
The _______ represents the number of seconds per cycle.
State the SI units for the period
- Round trip: final position and velocity must be the same as the initial values.
- period
- SI units: Seconds
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Define frequency (state SI units)
- Frequency, (f): represents the number of oscillations that the particle undergoes per unit time interval or number of cycles per time
- SI Units: s-1 or Hertz (Hz)
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State the formula and SI units for angular frequency
State the formula for frequency, and of period (2)
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Consider an object attached to a spring. The force described by Hooke's law is the _____ force in _______ _______ law:
State 3 Formulas for Fnet and one for acceleration ax
Why can't kinematic equation be applied?
- net force
- Newton's Second law
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- Because the acceleration is not constant
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If the block is released from some position x = A, the block continues to oscillate between -A and +A. These are ______ ______ of the motion. The force is ________. In the absence of friction, the motion will continue _______. Real systems are generally subject to _______ so they do not actually oscillate forever.
- turning points
- conservative
- forever
- friction
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Restate Hooke's Law by stating the formula for Fs and ax.
Then state the 2nd formula for angular frequency.
What is the 2nd derivative of x as it pertains to time (just another formula for acceleration when in SHM)
Solve for x(t) and identify each component:
The phase of the motion is the quantity ________
x(t) is periodic and its value is the same each time "ωt" increases by _____ radians
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There are 4 constants present list and explain each
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Formula for angular frequency (2)
Formula for period (3)
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The frequency and the period of any spring-mass system depend on which two factors?
They do not depend on the parameters of _______ (give three examples).
- Depends only on the mass of the particle and the force constant of the spring
- Does not depend on parameters of motion (amplitude, velocity, acceleration etc)
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If the frequency and period would depend on the amplitude, the motion is still _______ (explain), but NOT _______ _______ (state an example)
The frequency is larger for _______ springs (______ values of k) and ________ with increasing mass of the particle
- harmonic (meaning moving back and forth)
- simple harmonic (ex: bouncing ball)
- stiffer springs
- large
- decreases
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Describing a sine/cosine wave
State what type of curves these are and 3 ways in which they differ
State the formulas for:
θ
ω
T
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Finding the phase constant
A and Φ0 are determined uniquely by the ______ and _______ of the particle at t = 0 (_____ condition)
- position and velocity
- (initial condition)
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Finding the phase constant
State the formulas for:
x(t)
at t = 0, x(t =0) **(2 formulas)
at t = 0, v(t = 0) **(2 formulas)
v0/x0
A2
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- **pending edits on review of notes
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For simple harmonic motion, (d2x)/(dt2)= ______
State the expression for the following:
Expression for displacement
Expression for velocity
Expression for acceleration
Maximum displacement (also state where it occurs)
Maximum speed (also state where it occurs)
Maximum acceleration (also state where it occurs)
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C. Time Period depends on k/m not amplitude so it'll be the same frequency, meaning the same period So as a result time does not change
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Assume a spring mass system is moving on a frictionless surface, state the formula for:
Kinetic energy (2).
Elastic potential energy (2)
Because this is an isolated system, the total energy is _______. State the formula for energy with max potential energy (3-story) and the energy formula for max velocity
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State the formula for energy, then find the formula for velocity (2) (new one using an Energy Approach)
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For each of the following oscillations, state the the expected Kinetic energy, Potential energy and Total energy
*Bonus: Restate the formulas for Velocity using the energy approach
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