Q.
The displacement of a particle executing simple harmonic motion is given by y=A0 + A sin ωt + B cos ωtThen, the amplitude of its oscillation is given by
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a
A2+B2
b
A02+(A+B)2
c
A + B
d
A0 + A2+B2
answer is A.
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Detailed Solution
The displacement of given particle is y=A0 + A sin ωt + B cos ωt … (i)The general equation of SHM can be given as x = a sin ωt + b cos ωt … (ii)So, from Eqs. (i) and (ii), we can say that A0 be the value of mean position, at which y = 0.∴ Amplitude, R = A2+B2+2AB cos θAs two functions sine and cosine have phase difference of 90o.∴ R = A2+B2 (∵ cos 90°=0)
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