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» Solution :`Y=(F)/(A),(L)/(x_(1)) rArr x_(1)=(FL)/(AY), F=Kx_(2) rArr x_(2)=(F)/(K)` `X=x_(1)+x_(2)=(F(LK+AY))/(KAY) rArr x= ma((LK+AY))/(KAY), (x)/(a) m=((LK+AY))/(KAY) rArr T=2pi SQRT((x)/(a))` `T=2pi sqrt((m(LK+AY))/(KAY))`