One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a spring of spring constant K. A mass m hangs from the free end of the spring. The area of cross-section and Young.s modulus of the wire are A and Y respectivley. Find the time period with which the mass m will oscillate if it is slightly pulled down and released?

One end of a long metallic wire of length L is tied to the ceiling. Th

1.	One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a spring of spring constant K. A mass m hangs from the free end of the spring. The area of cross-section and Young.s modulus of the wire are A and Y respectivley. Find the time period with which the mass m will oscillate if it is slightly pulled down and released?
Answer» <html><body><p></p>Solution :`Y=(<a href="https://interviewquestions.tuteehub.com/tag/f-455800" style="font-weight:bold;" target="_blank" title="Click to know more about F">F</a>)/(A),(L)/(x_(1)) rArr x_(1)=(FL)/(AY), F=Kx_(2) rArr x_(2)=(F)/(<a href="https://interviewquestions.tuteehub.com/tag/k-527196" style="font-weight:bold;" target="_blank" title="Click to know more about K">K</a>)` <br/> `<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>=x_(1)+x_(2)=(F(LK+AY))/(KAY) rArr x= ma((LK+AY))/(KAY), (x)/(a) m=((LK+AY))/(KAY) rArr T=2pi <a href="https://interviewquestions.tuteehub.com/tag/sqrt-1223129" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT">SQRT</a>((x)/(a))` <br/> `T=2pi sqrt((m(LK+AY))/(KAY))`</body></html>