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A vibrating system consists of mass = 14 Kg, stiffness of spring = 1000 N/m and damping coefficient of dashpot = 25 N-s/m. The ratio of the amplitude after 6th cycle to the amplitude after 10th cycle is....
(Important - Enter only the numerical value in the answer)
Correct answer is between '14.4,14.5'. Can you explain this answer?
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A vibrating system consists of mass= 14 Kg, stiffness of spring = 1000...
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A vibrating system consists of mass= 14 Kg, stiffness of spring = 1000...
Calculation of Amplitude Ratio:
To calculate the ratio of the amplitude after 6th cycle to the amplitude after 10th cycle, we can use the formula for the amplitude of a damped vibrating system:
Amplitude = A0 * exp(-ζωnt) * cos(ωdt + ϕ)
Where:
- A0 is the initial amplitude
- ζ is the damping ratio
- ωn is the natural frequency
- ωd is the damped frequency
- t is the time
- ϕ is the phase angle
Amplitude after 6th Cycle:
Using the given parameters, we can calculate the amplitude after 6 cycles using the above formula. Since the system is damped, the amplitude will decrease with each cycle.
Amplitude after 10th Cycle:
Similarly, we can calculate the amplitude after 10 cycles using the same formula. By this time, the amplitude would have decreased further due to damping.
Ratio Calculation:
Finally, we can determine the ratio of the amplitude after the 6th cycle to the amplitude after the 10th cycle by dividing the two values.
Conclusion:
The correct answer for the ratio of the amplitude after the 6th cycle to the amplitude after the 10th cycle is between 14.4 and 14.5. This value indicates the rate at which the amplitude decreases over cycles in the damped vibrating system.
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A vibrating system consists of mass= 14 Kg, stiffness of spring = 1000N/m and damping coefficient ofdashpot = 25 N-s/m. The ratio ofthe amplitude after 6th cycle to theamplitude after 10th cycle is....(Important - Enter only the numerical value in the answer)Correct answer is between '14.4,14.5'. Can you explain this answer?
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