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  • Help me understand! A spring has a force constant K and a mass m is suspended from it. The spring is cut into half and the same a mss is suspended from one of the halves. If the frequency of oscillation in the first case is a, then the frequency in t

A spring has a force constant K and a mass m is suspended from it. The spring is cut into half and the same a mss is suspended from one of the halves. If the frequency of oscillation in the first case is a, then the frequency in the second case will be

  • Option 1)

    2 a    

  • Option 2)

    a

  • Option 3)

    a/2

  • Option 4)

    a\sqrt{2}

 

Answers (1)

best_answer

As we discussed in concept

Time period of oscillation for spring mass system -

T= 2\pi \sqrt{\frac{m}{K}}

- wherein

m = mass of block

K = spring constant

 

 T=2\pi \sqrt{\frac{m}{K}}\:=>\:f=\frac{1}{2\pi}\:\sqrt{\frac{K}{M}}

f_{1}\:=\:\frac{1}{2\pi}\sqrt{\frac{K}{m}}

when spring cut into two half then the force constant will be doubled.

f_{2}\:=\:\frac{1}{2\pi}\sqrt{\frac{2K}{m}}

\therefore\:\frac{f_{2}}{f_{1}}=\frac{\sqrt{2}}{1}\:=\:\therefore\:f_{2}=\sqrt{2}f_{1}


Option 1)

2 a    

This option is incorrect.

Option 2)

a

This option is incorrect.

Option 3)

a/2

This option is incorrect.

Option 4)

a\sqrt{2}

This option is correct.

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Plabita

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