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An undamped spring-mass system with mass m and spring stiffness k is shown in the figure. The natural frequency and natural period of this system are ω rad/s and T s. respectively. If the stiffness of the spring is doubled and the mass is halved, then the natural frequency and the natural period of the modified system, respectively, are
  • a)
    ω rad/s and T s 
  • b)
    ω/2 rad/s and 27 s 
  • c)
    4 ω rad/s and T/4 s
  • d)
    2 ω rad/s and T/2 s
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
An undamped spring-mass system with mass m and spring stiffness k is s...

Natural frequency, (ωk' = n
Time period, 
For new system m' = m/2
k' = 2k
∴ New natural frequency


∴ ω'n = 2ωn ⇒ Frequency will be double.
Now, new time period

∴ 2π/wn = Tn  
∴ T'n = Tn/2
Time period will become half.
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Most Upvoted Answer
An undamped spring-mass system with mass m and spring stiffness k is s...

Natural frequency, (ωk' = n
Time period, 
For new system m' = m/2
k' = 2k
∴ New natural frequency


∴ ω'n = 2ωn ⇒ Frequency will be double.
Now, new time period

∴ 2π/wn = Tn  
∴ T'n = Tn/2
Time period will become half.
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An undamped spring-mass system with mass m and spring stiffness k is shown in the figure. The natural frequency and natural period of this system are ω rad/s and T s. respectively. If the stiffness of the spring is doubled and the mass is halved, then the natural frequency and the natural period of the modified system, respectively, area)ω rad/s and T sb)ω/2 rad/s and 27 sc)4 ω rad/s and T/4 sd)2 ω rad/s and T/2 sCorrect answer is option 'D'. Can you explain this answer?
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An undamped spring-mass system with mass m and spring stiffness k is shown in the figure. The natural frequency and natural period of this system are ω rad/s and T s. respectively. If the stiffness of the spring is doubled and the mass is halved, then the natural frequency and the natural period of the modified system, respectively, area)ω rad/s and T sb)ω/2 rad/s and 27 sc)4 ω rad/s and T/4 sd)2 ω rad/s and T/2 sCorrect answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about An undamped spring-mass system with mass m and spring stiffness k is shown in the figure. The natural frequency and natural period of this system are ω rad/s and T s. respectively. If the stiffness of the spring is doubled and the mass is halved, then the natural frequency and the natural period of the modified system, respectively, area)ω rad/s and T sb)ω/2 rad/s and 27 sc)4 ω rad/s and T/4 sd)2 ω rad/s and T/2 sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An undamped spring-mass system with mass m and spring stiffness k is shown in the figure. The natural frequency and natural period of this system are ω rad/s and T s. respectively. If the stiffness of the spring is doubled and the mass is halved, then the natural frequency and the natural period of the modified system, respectively, area)ω rad/s and T sb)ω/2 rad/s and 27 sc)4 ω rad/s and T/4 sd)2 ω rad/s and T/2 sCorrect answer is option 'D'. Can you explain this answer?.
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