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Two particles executing SHM of same amplitude of 20cm with same period along the same line about same equilibrium position.the maximum distance between thr two is 20cm.their phase difference in radian is equal to?

Alia , 6 Years ago
Grade 12th pass
anser 1 Answers
Arun

Last Activity: 6 Years ago

Let equations of two SHMs be x=Asin(wt) and x=Asin(wt+a), where A,w, be common amplitude and angular frequency, and a be phase difference between two SHMs. 
distance between two particles at any time t =| A(sin(wt+a)-sin(wt))| 
=A*|2sin(a/2)cos((2wt+a)/2)| 
max value is when |cos((2wt+a)/2)|=1 
max distance=2A|sin(a/2)|=20cm=A; or, |sin(a/2)|=1/2 
or, sin(a/2)=1/2 or -1/2,  
a/2=pi/6 rad or -pi/6 rad 
a = pi/3 rad or -pi/3 rad. 
therefore SHMs have a phase difference of pi/3.

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