Two simple harmonic motions are given by: x1=asinωt+acosωt x2=asinωt+a√3cosωt The ratio of the amplitudes of first and second motion and the phase difference between them are respectively:
√32 and π6
√32 and π12
√32 and π12
2√3 and π12
A
√32 and π6
B
√32 and π12
C
2√3 and π12
D
√32 and π12
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Solution
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⇒x1=asinωt+acosωt=a√2sin(ωt+45)
⇒x2=asinωt+a√3cosωt=2a√3sin(ωt+30)
Using these equations above phasor diagrams are drawn.
Ratio of amplitude =a1a2=√3√2
Phase difference =π4−π6=π12
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