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In the given spring block system if k = ...

In the given spring block system if `k = 25 pi^(2) Nm^(-1)`, find time period of oscillation.

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The correct Answer is:
1
Equivalent spring constant `=k_(eq)= (2kxx(k)/(2))/(2k+(k)/(2))=(2k)/(5)`
Reduced mass of system `= mu =(5xx5)/(5+5) = (5)/(2)`
`:. T =2pi sqrt((mu)/(k_(eq))) =2pi sqrt((.^(5)//_(2))/(.^(2k)//_(5))) =5pi sqrt((1)/(k)) =5pi sqrt((1)/(25pi^(2))) =1s`
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Knowledge Check

  • In a spring block system if length of the spring is reduced by 1% , then time period

    A
    increase by `2%`
    B
    increase by `0.5%`
    C
    decrease by `2%`
    D
    decrease by `0.5%`
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