The time period of a mass loaded spring is 'T' If 20% of its turns are cut and - Physics - Oscillations

Question

The time period of a mass loaded spring is 'T' If 20% of its turns
are cut and removed, then with what time period the same mass
attached to the remaining spring would oscillate?

Sanjay Singh · Accepted Answer

Dear student
We know that time period of spring mass system is T=2πmk 
1 ( m is mass of block and  k is spring constant) Let length of spring is L
When the length is cut by 20 percent than length of remaining spring is (L-L5)=4L5Spring constant is inversely proportional to natural length ofspring  so product of spring constant and length of spring is constant
 K×L=constantK×L=K1×4L5  (K1 is spring constant of spring after it is cut)K1=5K4so time period isT1=2πmK1=2π4m5KT1=2πmK (25)
2comparing eqn  2  with eqn 
1T1=T (25)Regards

The time period of a mass loaded spring is 'T' . If 20% of its turns are cut and removed, then with what time period the same mass attached to the remaining spring would oscillate?