Two simple harmonic motions are represented by `y_1=4 sin (4 pi t+pi//2) and y_2=3 cos (4 pi t)` The resultant amplitude is

Options

A. a)7
B. b)1
C. c)3
D. d)`2+sqrt3`

Answer

A

Explanation

Given `y_1= 4 sin (4 pi t+pi/2)`
or `y_1=4 cos 4 pi t`
and `y_2=3 cos 4 pi t`
Resultant `y=y_1+y_2`
`y=4 cos 4 pi t+3 cos 4 pi t`
`y=7 cos 4 pi t`
`therefore` Resultant amplitude
a=7