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A spring-mass suspension has a natural frequency of 40 rad/s. What is the damping ratio required if it is desired to reduce this frequency to 20 rad/s by adding a damper to it?
  • a)
    √3/2
  • b)
    1/2
  • c)
    1/√2
  • d)
    1/4
Correct answer is option 'A'. Can you explain this answer?
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A spring-mass suspension has a natural frequency of 40 rad/s. What is ...
We can use the formula for natural frequency with damping:

ωn = ω0 √(1 - ζ^2)

where:
ωn = natural frequency with damping
ω0 = natural frequency without damping (given as 40 rad/s)
ζ = damping ratio (unknown)

We can rearrange this formula to solve for ζ:

ζ = √(1 - (ωn/ω0)^2)

Substituting the given values:

ζ = √(1 - (20/40)^2) = √(1 - 0.25) = 0.866

Therefore, the damping ratio required to reduce the natural frequency from 40 rad/s to 20 rad/s is 0.866.
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