SHMMedium
Question
An osculation is described by the equation x = A sin 2πγ2t where A changes with time according to the law A = A0 (1 + cos 2πγ2t) where A0 is constant. Find the ration of frequencies of harmonic oscillations forming oscillation
Options
A.γ1 : γ2 : (γ1 - γ2)
B.γ1 : (γ1 - γ2) : (γ1 + γ2)
C.γ1 : γ2 : (γ2 - γ1)
D.γ1 : γ2 : (γ1 + γ2)
Solution
x = A0(1 + cos 2πγ2t) sin (2πγ1t)
= A0[sin 2πγ1t + cos 2πγ2t + sin 2πγ1t]
= A0[sin 2πγ1t +
sin (2π(γ1 + γ2)t - 
sin (2π(γ1 - γ2)t))]
Required ratio ν1 : (ν1 - ν2) : (ν1 + ν2)
= A0[sin 2πγ1t + cos 2πγ2t + sin 2πγ1t]
= A0[sin 2πγ1t +
sin (2π(γ1 + γ2)t - sin (2π(γ1 - γ2)t))]Required ratio ν1 : (ν1 - ν2) : (ν1 + ν2)
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