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

Answer» <html><body><p></p>Solution :Given situation are <a href="https://interviewquestions.tuteehub.com/tag/shown-1206565" style="font-weight:bold;" target="_blank" title="Click to know more about SHOWN">SHOWN</a> in given below figures (i) and (ii) <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P2_C14_E04_034_S01.png" width="80%"/> <br/> <a href="https://interviewquestions.tuteehub.com/tag/suppose-656311" style="font-weight:bold;" target="_blank" title="Click to know more about SUPPOSE">SUPPOSE</a> both the pendulums follows the below functions, <br/> `theta_(1) = theta_(<a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>) sin (omega t+ phi_(1))"""…….."(1)` <br/> `theta_(2) = theta_(0) sin (omega t+phi_(2))"""........."(2)` <br/> where, `theta_(0)=` amplitude <br/> For first pendulum at any time t, <br/> `theta_(1)= +theta_(0)""` (Right side) <br/> From equation (1) <br/> `+ theta_(1)= theta_(0) sin (omega t+phi_(1))` <br/> `<a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a> +1 = sin(omega t+phi_(1))` <br/> `therefore omega t + phi_(1) = (pi)/(2)""".........."(3)` <br/> Similarly for second pendulum at time t, <br/> `theta_(2) = -(theta_0)/(2)""` (left side) <br/> From equation (2) <br/> `-(theta_0)/(2)= theta_(0) sin (omega t+ phi_(2))` <br/> `therefore -(1)/(2)= sin (omega t+ phi_(2))` <br/> `therefore omega +phi_(2)= -(pi)/(6)" or "(7pi)/(6)"""......."(4)[i.e. = 2pi-(pi)/(6)]` <br/> the difference in phases from equ. (3) and (4) <br/> `(omega + phi_(2))-(omega t-phi_(1))= (7pi)/(6)-(pi)/(2)` <br/> `therefore phi_(2)-phi_(1)= (<a href="https://interviewquestions.tuteehub.com/tag/4pi-1882352" style="font-weight:bold;" target="_blank" title="Click to know more about 4PI">4PI</a>)/(6)= (2pi)/(3)` <br/> `therefore phi_(2)-phi_(1)= 120^(@)`.</body></html>


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