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Question

A spring is loaded with two blocks m1 and m2 where m1 is rigidly fixed with the spring and m2 is just kept on the block m1 as shown in the figure. The maximum energy of oscillation that is possible for the system having the block m2 in contact with m1 is

  1. fraction numerator m subscript 1 end subscript superscript 2 end superscript g to the power of 2 end exponent over denominator 2 k end fraction    
  2. fraction numerator m subscript 2 end subscript superscript 2 end superscript g to the power of 2 end exponent over denominator 2 k end fraction    
  3. fraction numerator left parenthesis m subscript 1 end subscript plus m subscript 2 end subscript right parenthesis to the power of 2 end exponent g to the power of 2 end exponent over denominator 2 k end fraction    
  4. None of these    

The correct answer is: fraction numerator left parenthesis m subscript 1 end subscript plus m subscript 2 end subscript right parenthesis to the power of 2 end exponent g to the power of 2 end exponent over denominator 2 k end fraction


    Let the required amplitude be A. For this amplitude of oscillation the normal contact force between the blocks can be given as
    m2 g – N = m2 a where a = w2A
    Þ m2g – N = m2w2 A
    Putting N = 0 for just losing contact for maximum amplitude, we obtain
    A = fraction numerator g over denominator omega to the power of 2 end exponent end fraction where w = angular frequency of oscillation of (m1 + m2 ) and the spring.
    Putting w2 = fraction numerator k over denominator m subscript 1 end subscript plus m subscript 2 end subscript end fraction, we obtain
    A = fraction numerator left parenthesis m subscript 1 end subscript plus m subscript 2 end subscript right parenthesis g over denominator k end fraction
    \ Umax = fraction numerator 1 over denominator 2 end fractionkA2 = fraction numerator left parenthesis m subscript 1 end subscript plus m subscript 2 end subscript right parenthesis to the power of 2 end exponent g to the power of 2 end exponent over denominator 2 k end fraction.

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