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Natural frequency of undamped free vibration is 100 rps and damping is provided with damping factor is 0.8 then what is the frequency of damped vibration
- a)80 rps
- b)45 rps
- c)60 rps
- d)96 rps
Correct answer is option 'C'. Can you explain this answer?
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Natural frequency of undamped free vibration is 100 rps and damping is...
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Natural frequency of undamped free vibration is 100 rps and damping is...
Natural frequency of undamped free vibration is the frequency at which a system vibrates when there is no damping present. It is determined by the stiffness and mass of the system.
Given:
Natural frequency of undamped free vibration = 100 rps
Damping factor = 0.8
To find: Frequency of damped vibration
When damping is present, the frequency of vibration decreases due to the dissipation of energy. The relationship between the natural frequency and the damped frequency is given by the formula:
Damped frequency = Natural frequency * sqrt(1 - damping factor^2)
Let's substitute the given values into the formula:
Damped frequency = 100 * sqrt(1 - 0.8^2)
Calculating the value inside the square root:
1 - 0.8^2 = 1 - 0.64 = 0.36
Taking the square root of 0.36:
sqrt(0.36) = 0.6
Now, substituting this value back into the formula:
Damped frequency = 100 * 0.6 = 60 rps
Therefore, the frequency of damped vibration is 60 rps, which corresponds to option C.
Given:
Natural frequency of undamped free vibration = 100 rps
Damping factor = 0.8
To find: Frequency of damped vibration
When damping is present, the frequency of vibration decreases due to the dissipation of energy. The relationship between the natural frequency and the damped frequency is given by the formula:
Damped frequency = Natural frequency * sqrt(1 - damping factor^2)
Let's substitute the given values into the formula:
Damped frequency = 100 * sqrt(1 - 0.8^2)
Calculating the value inside the square root:
1 - 0.8^2 = 1 - 0.64 = 0.36
Taking the square root of 0.36:
sqrt(0.36) = 0.6
Now, substituting this value back into the formula:
Damped frequency = 100 * 0.6 = 60 rps
Therefore, the frequency of damped vibration is 60 rps, which corresponds to option C.
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Natural frequency of undamped free vibration is 100 rps and damping is provided with damping factor is 0.8 then what is the frequency of damped vibrationa)80 rpsb)45 rpsc)60 rpsd)96 rpsCorrect answer is option 'C'. Can you explain this answer?
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