Question

A particle of mass `2kg` moves under a force given by
`vec(F)=-(8N//m)(xhat(i)+yhat(j))`
where `hat(i)` and `hat(j)` are unit vectors in the `x` and `y` directions.
The particle is projected from the origin in `xy` plane with an initial velocity `vec(v)=(3m//s)hat(i)+(4m//s)hat(j)`.
Select correct statement(s).
A. Time after which the particle will return to origin first timeis `pi//2` sec
B. Time after which the particle will return to origin first time is `pi` sec
C. The maximum disance between the particle and origin is `2m`
D. The maximum distance between the particle and origin is `2.5m`

Answer 1

Correct Answer - A::D
The `x` and `y` both coordinates oscillates simple harmonically is same plane.
`omega =sqrt(k/m)=1rad//s`
`T=pis`
`A_(x)=(u_(x))/(omega)=1.5m`
`A_(y)=(u_(y))/(omega)=2m`
Net amplitude `=sqrt(A_(x)^(2)+A_(y)^(2))=2.5m`