Wave Motion> two particles executes SHM of Same amplit...

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

Kavan , 7 Years ago

Grade 11

2 Answers

Gaurav Gupta

Last Activity: 7 Years ago

Approved

Arun

Last Activity: 7 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)

Approved