1.

Two simple harmonic motions are represented by y_(1)=5[sin2pit+sqrt(3))cos2pi t] and y_(2)=5sin(2pit+(pi)/(4)). The ratio of their amplitude is :

Answer»

`1:3`
`sqrt(3):1`
`1:1`
`2:1`

Solution :`y_(1)=5[sin 2pi t+sqrt(3)cos 2pi t]`
`=10[(1)/(2)sin 2pi t+(sqrt(3))/(2)cos 2pi t]`
`=10[cos""(pi)/(3)sin2pi t+sin""(pi)/(3)cos 2pi t]`
`y_(1)=10 sin(2pi t+(pi)/(3))`
`y_(2)=5sin(2pi t+(pi)/(4))`
So ratio of amplitude of `y_(1)` and `y_(2)` is `(10)/(5)=(2)/(1)`
So CORRECT choice is (d).


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