question_answer

Two particles execute SHM on same straight line with same mean position, same time period 6 second and same amplitude 5cm. Both the particles start SHM from their mean position (in same direction) with a time gap of 1 second. The maximum separation between the two particles during their motion is  

A) 2cm

B) 3cm

C) 4cm

D) 5cm

Correct Answer: D

Solution :

[d] Figure shows the mapping of the two SHMs with circular motions having phase difference \[\phi =\omega t=\frac{2\pi }{6}\times 1=\frac{\pi }{3}rad\] The maximum separation between the two particles is \[{{S}_{\max }}=2A\,\sin \,\frac{\pi }{6}\] \[or\,\,\,{{S}_{\max }}=2\times 5\times \frac{1}{2}=5cm.\]