A body of mass `1kg` is suspended from a weightless spring having force constant `600N//m`. Another body of mass `0.5 kg` moving vertically upward hits the suspended body with a velocity of `3.0m//s` and get embedded in it. Find the frequency of oscillations and amplitude of motion.

Options

A. `(10)/(pi)Hz,10Cm`
B. `(10)/(pi)Hz,5Cm`
C. `(5)/(pi)Hz,5Cm`
D. `(5)/(pi)Hz,10Cm`

Answer

B

Explanation

`V=(0.5xx3)/((0.5+1))=1m//simpliesK_(max)=U_(max)`
`(1)/(2)xx1.5xx1^(2)=(1)/(2)xx600xxA^(2)`
`A=5cm`
`f=(1)/(2pi)sqrt((k)/(m))=(1)/(2pi)sqrt((600)/(1.5))=(10)/(pi)`
`f=(10)/(pi)Hz`