Answered: Find the personal frequency, shape mode…

Find the personal frequency, shape mode and vibration response equation of the above system, if K1 250 N / m, K2 = 250 N / m =, K3 = 300 N / m, K4 = 350 N / m = K5 = 200 N / m

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Question

Find the personal frequency, shape mode and vibration response equation of the above system, if K1 250 N / m, K2 = 250 N / m =, K3 = 300 N / m, K4 = 350 N / m = K5 = 200 N / m

Expert Solution

Step 1

The spring-mass system has its own natural frequency. A more complex system has several natural frequencies.

Here there are two masses attached to the system. For mass m₁

$ω_{1} = \sqrt{\frac{k_{3}}{m_{1}}} = \sqrt{\frac{300}{5}} = 7.456 r a d / s$ .

For m₂

$k = (\frac{k_{1} k_{2}}{k_{1} + k_{2}}) + (\frac{k_{3} k_{4}}{k_{3} + k_{4}}) + k_{5} k = (125) + (161.54) + 200 = 486.54 N / m ω_{2} = \sqrt{\frac{486.54}{10}} = 6.975 r a d / s$

But a system with more than one natural frequency will not vibrate harmonically.

consider two-mass system is vibrating, then we can write

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