The displacement eqution of a particle is `x=3 sin 2t + 4 cos 2t`. The amplitude and maximum velocity will be respetively

Options

A. 5,10
B. 3,2
C. 4,2
D. 3,4

Answer

A

Explanation

`x=3 sin 2t+ 4 cos 2t`
from given eqution.
`a_(1)=3, a_(2)=4, and phi=(pi)/(2)`
`:.a=sqrt(a_(1)^(2)+a_(2)^(2))= sqrt(3^(2)+4^(2))`
`=5`
`V_("max")= a omega=5xx2=10`