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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?

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?

Grade:12th pass

1 Answers

Arun
25750 Points
5 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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