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)
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 _______
- Common examples:
- 1) Object undergoing uniform circular motion
- 2) A mass oscillating on a spring
- 3) A pendulum
- period or frequency
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
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
- "ignore gravity"
Explain how the force exerted by the spring will act in each of these scenarios
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
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
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.
- SI units: Seconds
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)
State the formula and SI units for angular frequency
State the formula for frequency, and of period (2)
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
- Because the acceleration is not constant
Label the diagrams
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
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
There are 4 constants present list and explain each
Formula for angular frequency (2)
Formula for period (3)
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)
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
Describing a sine/cosine wave
State what type of curves these are and 3 ways in which they differ
State the formulas for:
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)
Finding the phase constant
State the formulas for:
at t = 0, x(t =0) **(2 formulas)
at t = 0, v(t = 0) **(2 formulas)
- **pending edits on review of notes
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)
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
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
Label the diagram
State the formula for energy, then find the formula for velocity (2) (new one using an Energy Approach)
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