SDOF Systems

Question 1

What is a SDOF

Answer 1

Single Degree of Freedom system:

• one mass that can move in 1 direction
• 1 equation of motion
• 1 Wn and 1 Wr

Question 2

What will response be of SDOF in free vibration

Answer 2

System will vibrate at its natural frequency

Question 3

What will response be of SDOF in forced vibration

Answer 3

System will in same frequency as forced, largest response at resonance

Question 4

Equation of motion for mass-spring SDOF system

Answer 4

mx(2dot) + kx = 0 
or 
mx(2dot) + kx = Fsin(vt)

• assume x = Asin(wt)

Wn = SQRT(k/m)

Question 5

What is the FRF

Answer 5

Frequency Response Function

Magnitude component of FRF = The ratio of the input force, F, to the response amplitude A

magnitude component = A/F = 1 / (-Mv^2 + k )

Question 6

If there is no damping what is the amplitude at resonance

Answer 6

infinite

Question 7

Equation of motion including damping

Answer 7

mx(2dot) + cx(dot) + kx = 0

Question 8

What exponential can be assumed as a solution

Answer 8

x = Xe^st

if underdamped

x = Xe^iwt

if ms^s + cs + k = 0
s1,2 = quatratic

x = X1 e^(s1t) + X2e^(s2t)

Question 9

Equation for damping ratio

Answer 9

ζ = C / Cc

ζ = damping / critical damping

Question 10

Equation for natural damping frequency

Answer 10

Wd = Wn x SQRT( 1 - ζ^2 )

Question 11

How to solve damping forced vibration

Answer 11

Must be solved in 2 parts:

• free vibration problem
• particular integral

Forced vibration response will be a combination of steady state (sinusoid) and a transient response (decaying sinusoid)

• can use force diagrams to find this out

Question 12

What is a steady state response

Answer 12

same frequency as as forced vibration - don’t know the phase or amplitude though