200 kg द्रव्यमान और 80 N/mm कठोरता वाले स्प्रिंग से युक्त एक कंपन प्रणाली की अल्पावयवित कंपन की वृत्ताकार आवृत्ति है:

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BHEL Engineer Trainee Mechanical 24 Aug 2023 Official Paper
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  1. 20 rad/s
  2. 40 rad/s
  3. 80 rad/s
  4. 60 rad/s

Answer (Detailed Solution Below)

Option 1 : 20 rad/s
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संप्रत्यय:

अल्पावयवित मुक्त कंपनों के लिए वृत्ताकार आवृत्ति (रेडियन/सेकंड में प्राकृतिक आवृत्ति) निम्न द्वारा दी जाती है:

\( \omega_n = \sqrt{\frac{k}{m}} \)

जहाँ,

  • \( k \) = स्प्रिंग की कठोरता (N/m में)
  • \( m \) = द्रव्यमान (kg में)

दिया गया है:

द्रव्यमान, \( m = 200~\text{kg} \)

कठोरता, \( k = 80~\text{N/mm} = 80 \times 10^3~\text{N/m} \)

परिकलन:

\( \omega_n = \sqrt{\frac{80 \times 10^3}{200}} = \sqrt{400} = 20~\text{rad/s} \)

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