The position of a particle with respect to origin varies according to the relation x=3sin⁡100t+8cos2⁡50t.The maximum displacement of the particle from the origin is ____________.

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answer is 9.

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Detailed Solution

x=3sin⁡100t+8cos2⁡50t=3sin⁡100t+8[1+cos⁡100t]2x=4+3sin⁡100t+4cos⁡100t(x−4)=5sin⁡(100t+ϕ)tan⁡ϕ=43 Amplitude =5 units Maximum displacement =9 units

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