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Question

Four massless springs of force constant 2K, 2K, K and 2K are connected to a mass M lying on a smooth horizontal surface as shown in the figure. If the mass M is displaced horizontally through a small distance and released, the system will oscillate with a frequency

  1. fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator 7 K over denominator M end fraction end root    
  2. fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator 4 K over denominator M end fraction end root    
  3. fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator K over denominator 3 M end fraction end root    
  4. fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator K over denominator 4 M end fraction end root    

The correct answer is: fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator 4 K over denominator M end fraction end root


    K subscript e q end subscript equals 4 k rightwards double arrow f equals fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator 4 K over denominator M end fraction end root

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