SHMHard
Question
One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring constant k. A mass m hangs freely from the free end of the spring. The area of cross-section and the Young′s modulus of the wire are A and Y respectively. If the mass is slighly pulled down and released, it will oscillate with a time period T equal to
Options
A.2π(m/k)1/2
B.
C.2π[(mYA / kL)1/2]
D.2π[(mY / YA)1/2]
Solution
Keq =
= 
= 
∴ T =
= 
Note : Equivalent force constant for a wire is given by k =
. Because in case of a wire, F = 
ᐃL and in case of spring F = k. ᐃL. Comparing these two, we kind k of wire = 
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