Consider a pair of identical pendulums,which | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the angular displacement of the two pendulums be given by:$	heta_1 = 	heta_0 \sin(\omega t + \phi_1)$$	heta_2 = 	heta_0 \sin(\omega t + \p

Vedclass · Accepted Answer

$2\pi/3$

Vedclass · Answer

(A) Let the angular displacement of the two pendulums be given by:$	heta_1 = 	heta_0 \sin(\omega t + \phi_1)$$	heta_2 = 	heta_0 \sin(\omega t + \phi_2)$where $	heta_0$ is the amplitude. Since the pendulums are identical and oscillate with equal amplitude,$	heta_0 = 2^o$.For the first pendulum at its extreme right position:$	heta_1 = +	heta_0 = 2^o$$2^o = 2^o \sin(\omega t + \phi_1) \implies \sin(\omega t + \phi_1) = 1 \implies \omega t + \phi_1 = \pi/2$For the second pendulum at $1^o$ to the left:$	heta_2 = -1^o = -	heta_0/2 = -2^o/2$$-2^o/2 = 2^o \sin(\omega t + \phi_2) \implies \sin(\omega t + \phi_2) = -1/2$Thus,$\omega t + \phi_2 = -\pi/6$ or $7\pi/6$.Taking $\omega t + \phi_2 = -\pi/6$,the phase difference $\Delta \phi = |(\omega t + \phi_1) - (\omega t + \phi_2)| = |\pi/2 - (-\pi/6)| = |\pi/2 + \pi/6| = |3\pi/6 + \pi/6| = 4\pi/6 = 2\pi/3$.

Similar Questions

Two particles $A$ and $B$ execute $SHMs$ of periods $T$ and $\frac{3T}{2}$. If they start from the mean position,then the phase difference between them,when the particle $A$ completes two oscillations,will be

After the beginning of motion,how long will it take for a harmonically oscillating particle to reach a displacement equal to one-half of its amplitude,if the time period is $24 \ sec$ and the particle starts from rest?

The equation of $S.H.M.$ is $y = a \sin(2\pi nt + \alpha)$,then its phase at time $t$ is:

Two particles are executing $S.H.M.$ of same amplitude and frequency along the same straight line path. They pass each other when going in opposite directions,each time their displacement is half of their amplitude. What is the phase difference between them?

Vedclass Test Series

Exam Paper Generator

Online Exam Module