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  • Help me understand! Two springs of constants k1 and k2 equal maximum velocities, when executing simple harmonic motion. The ratio of their amplitudes (masses are equal) will be

Two springs of constants k1 and k2 equal maximum velocities, when executing simple harmonic motion. The ratio of their amplitudes (masses are equal) will be
 

  • Option 1)  k1/k2 
  • Option 2) k2/k1  
  • Option 3) ( k1/k2)(1/2) 
  • Option 4) (k2/k1 )(1/2) 
 

Answers (1)

As learnt in

Relation of velocity and displacement -

v= w\sqrt{A^{2}-x^{2}}
 

- wherein

\rightarrow  x is displacement from mean position

\rightarrow  A is Amplitude.

 

 v = Aw = A\sqrt{\frac{k}{m}}

v_{1} = A_{1} \sqrt{\frac{k_{1}}{m}}                            v_{1} = v_{2}

v_{2} = A_{2}\sqrt{\frac{k_{2}}{m}}                           A_{1}\sqrt{\frac{k_{1}}{m}} = A_{2}\sqrt{\frac{k_{2}}{m}}

\therefore \frac{A_{1}}{A_{2}} = \sqrt{\frac{k_{2}}{k_{1}}}


Option 1)

\frac{k_1}{k_2}

This option is incorrect

Option 2)

\frac{k_2}{k_1}

This option is incorrect

Option 3)

(\frac{k_1}{k_2})^{\frac{1}{2}}

This option is incorrect

Option 4)

(\frac{k_2}{k_1})^{\frac{1}{2}}

This option is correct

Posted by

Vakul

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