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two particles executes SHM of Same amplitude of20cm with same period along the Sam line about the Same equilibrium position. The maximum distance between two is 20 cm. Their phase difference in radian is. A. 120 B.90 C.60 D.45

two particles executes SHM of Same amplitude of20cm with same period along the Sam line about the Same equilibrium position. The maximum distance between two is 20 cm. Their phase difference in radian is.
A. 120
B.90
C.60
D.45

Grade:11

2 Answers

Gaurav Gupta
askIITians Faculty 686 Points
3 years ago
564-217_phas.JPG
Arun
25768 Points
3 years ago
Dear student
 
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.
 
Regards
Arun (askIITians forum expert)

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