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Two point masses of 3.0kg and 1.0kg are ...

Two point masses of `3.0kg` and `1.0kg` are attached to opposite ends of a horizontal spring whose spring constant is `3Nm^(-1)` as shown in figure . The natural frequency of vibration so this system is `n//piHz`. Find the integral value of `n`.

Text Solution

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The correct Answer is:
1
The reduced mass of the system,
`m=(m_(1)xxm_(2))/(m_(1)+m_(2))=(3xx1)/(3+1)=(3)/(4)kg`
So, inertia factor, `m=(3)/(4)kg.`
Here, spring factor, `k=3Nm^(-1)`
Frequency `v=(1)/(2pi)sqrt((spri ngfact o r)/(i n ertia fact o r))`
`=(1)/(2pi)sqrt((3)/((3//4)))=(1)/(pi)Hz`
As per question, `(n)/(pi)=(1)/(pi)` or `n=1`
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