The displacement of a particle performing SHM `x= 3sin 2t+4 cos 2t`. The amplitude and maximum velocity of a particle respectively are………….

Options

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

Answer

A

Explanation

`x= 3 sin 2t + 4 cos 2t`
`a_(1)= 3, a_(2)= 4" and "phi= (pi)/(2)`
`therefore A= sqrt(a_(1)^(2)+a_(2)^(2))= sqrt(3^(2)+4^(2))= 5` unit
`implies v_("max")= A omega`
`= 5xx 2 = 10`.