When a mass m is attached to a spring, it normally extends by 0.2 m . The mass m is given a slight addition extension and released, then its time period will be

Options

A. `(2pi)/(7) sec`
B. `(2)/(3pi ) sec`
C. 1 sec
D. `(1)/(7) sec`

Answer

A

Explanation

For the spring, the weight (mg) produces an extension of 0.2m.
`because F=Kx and F=mg therefore mg=Kx therefore (m)/(K)=(x)/(g)`
`therefore T=2pi sqrt((m)/(K))=2pi sqrt((x)/(g))=2pi sqrt((0.2)/(9.8))`
`=2pi sqrt((1)/(49))=(2pi)/(7)s`