Two simple harmonic motions are represented by the equations.
`y_(1)=10"sin"(pi)/(4)(12t+1),y_(2)=5(sin3pt+sqrt(3)cos3pt)` the ratio of their amplitudes is

Options

A. `1:1`
B. `1:2`
C. `3:2`
D. `2:3`

Answer

A

Explanation

Here, `y_(1)=10"sin"(pi)/(4)(12t+1)`
or `y_(1)=10sin(3pit+(pi)/(4))` . . . (i)
and `y_(2)=5(sin3pit+sqrt(3)cos3pit)`
or `=10(sin3pitxx(1)/(2)+cos3pitxx(sqrt(3))/(2))`
`implies y_(2)=10sin(3pit+(pi)/(3))` . . . (ii)
Comparing equation (i) and (ii) with standard equation for SHM we get
`A_(1)=10 and A_(2)=10 " "because(A_(1))/(A_(2))=(10)/(10)=1/1`