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A simple harmonic oscillator consists of a panicle of mass in and an ideal spring with spring constant k. The particle oscillates with a time period T. The spring is cut into two equal parts. If one part oscillates with the same particle, the time period will be
  • a)
    2T
  • b)
    √2T
  • c)
    T / √2
  • d)
    T/2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A simple harmonic oscillator consists of a panicle of mass in and an i...
Explanation:

Concept:
- The time period of a simple harmonic oscillator is given by T = 2π√(m/k), where m is the mass of the particle and k is the spring constant.

When the spring is cut into two equal parts:
- When the spring is cut into two equal parts, the spring constant of each part becomes k/2.
- Due to conservation of energy, the time period of oscillation remains the same.

Calculation:
- For the original system with the full spring, T = 2π√(m/k).
- For each part of the spring after cutting, T' = 2π√(m/(k/2)) = 2π√(2m/k).
- Therefore, the new time period T' = T/√2.

Conclusion:
- When one part of the spring oscillates with the same particle, the time period of oscillation becomes T/√2.
- Hence, the correct answer is option 'C' - T/√2.
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Community Answer
A simple harmonic oscillator consists of a panicle of mass in and an i...
T/2.
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A simple harmonic oscillator consists of a panicle of mass in and an ideal spring with spring constant k. The particle oscillates with a time period T. The spring is cut into two equal parts. If one part oscillates with the same particle, the time period will bea)2Tb)√2Tc)T / √2d)T/2Correct answer is option 'C'. Can you explain this answer?
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