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A particle at the end of a spring executes simple harmonic motion with a period t 1 , while the corresponding period for another spring is t 2 . If the period of oscillation with the two springs in series is T , then -

Options

  1. AT = t 1 + t 2
  2. BT 2 = t 1 2 + t 2 2
  3. CT - 1 = t 1 - 1 + t 2 - 1
  4. DT - 2 = t 1 - 2 + t 2 - 2

Correct answer

B. T 2 = t 1 2 + t 2 2

Step-by-step solution

t 1 = 2 π m k 1   … . i ,   t 2 = 2 π m k 2   … . i i when springs are in series then T = 2 π m k 1 k 2 k 1 + k 2 = 2 π m k 1 + k 2 k 1 k 2 squaring and adding (i) and (ii) we get t 1 2 + t 2 2 = 4 π 2 m k 1 + 4 π 2 m k 2 = 4 π 2 m   k 1 + k 2 k 1 k 2 or t 1 2 + t 2 2 = T 2

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