The amplitude and maximum velocity will be respectively `X= 3 sin 2t + 4 cos 2t`The amplitude and maximum velocity will be respectively

Options

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

Answer

A

Explanation

`x = 3 sin 2 t + 4 cos 2 t`.
From given equation, `a_(1) = 3, a_(2)=4 and x = 3 sin 2t + 4 cos 2t`
`sqrt(3^(2)+4^(2))[(3)/(sqrt(3^(2)+4^(2))).sin 2t + (4)/(sqrt(3^(2)+4^(2)))cos 2t]`
`5[(5)/(3)sin 2t + (4)/(5)cos 2 t]`
`= 5 [sin 2 t cos alpha + sin alpha cos 2 t]`
`therefore" "cos alpha = (3)/(5) and sin alpha = (4)/(5)`

`therefore" "x = 5.[sin 2t.cos alpha + sin alpha. cos 2 t]`
`= 5 sin (2t + alpha)`
`therefore" "omega = 2 and alpha = 5`
`because" "[sin(A+B) = sin A cos B + cos A sin B]`
`rArr" "V_(max) = a omega = 5 xx 2 = 10`