Section 4.11  A Closer Look at Free Mechanical Vibrations

• to be able to determine the equation of motion of a mass attached to a spring with no damping or external force
• to be able to determine the equation of motion of a mass attached to a spring in the underdamped, critically damped, and overdamped cases

• undamped, free case

 
• simple harmonic motion
• period

 
• natural frequency

 
• angular frequency

 
• underdamped case

 
• damping factor

 
• quasiperiod

 
• quasifrequency

 
• overdamped case

 
• critically damped case
 

• finding the equation of motion of a mass, along with the amplitude, period, frequency, and length of time to reach the equilibrium position, #1

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• equations of motion in the underdamped, critically damped, overdamped cases, #6

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• underdamped case: determining the damping factor, quasiperiod, quasifrequency,#7

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• determining the maximum displacement of a mass, #11

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

QUESTION OF THE DAY

Find .

SOLUTION