In a linear system, an input of 5 sin ωt produces an output

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In a linear system, an input of 5 sin ωt produces an output of 10 cos ωt. The output corresponding to input 10 cos ωt will be equal to:

1. + 5 sin ωt
2. – 5 sin ωt
3. + 20 sin ωt
4. – 20 sin ωt

Correct Option: D

According to the problem
5 sin ωt → 10cos ωt
or
sin ωt → 2 cos ωt …(i)
differentiating equation (i)
cost ωt → – 2sin ωt
∴ an input of 10 cos ωt will cause a response of – 20 sin ωt.