We consider two rotors given by the angles 1 and 2 . (a) Assume their

We consider two rotors given by the angles θ₁ and θ₂.

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(a) Assume their time evolution is given by do =1+(02-01) dt d02 =w2+(01-02). dt (7.22) Write down the equation for the time evolution of the difference A = 01-02. Solve this equation and show that for any value of > 0, synchronisation will happen as t with a constant so-called phase lag where 0 = 82 (w2w1)/(2). (b) Now consider the following somewhat unusual time evolution: d01 dt = (7.23) d02 dt = w02 + (01-02). > w/2 synchronisation will happens, whereas for