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Consider a pair of identical pendulums, which oscillate with equal amplitude independently such that when on pendulum is at its extreme position making an angle of 2º to the right with the vertical. The other pendulum makes an angle of 1º to the left of the vertical. What is the phase difference between the pendulums?

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suppose θ0 is Angular amplitude of each of the pendulums.

θ1θ0 sin(wt + δ1

θ2 = θ0 sin(wt + δ2) {SHM of pendulums}

One pendulum is making 2º angle with vertical, θ0 = 2º.

For I pendulum θ1 = 2º 

∴ 2º = 2º sin (wt + δ1)

sin (wt + δ1) = 1

wt + δ1 = 90º 

For other pendulum, θ2 = −1º 

∴ −1º = 2º sin (wt + δ2)

or sin (wt + δ2) = − \(\frac{1}{2}\)

wt + δ2 = −30º  

∴ (wt + δ1) − (wt + δ2 ) = 90º −(−30º )

δ1δ2 = 120º

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