A spring mass system is executing simple harmonic motion. The equation of motion is given by y=8sinωt+6cosωt. The amplitude of the resultant is

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10 units

14 units

24 units

2 units

answer is A.

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Detailed Solution

resultant amplitude=R=a2+b2+2abcosϕ here a, b are amplitudes, ∅ is phase differenceThe given equation can be written as y=8sinωt+6sinωt+π2Here ϕ=π2; a=8; b=6, substituteR=82+62+2×8×6cosπ2 R=82+62 R=64+36 R=100=10 units

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