Question

Two particles execute SHM of same amplitude of 20 cm with same period along the same line about the same equilibrium position .The maximum distance between two is 20 cm .then their phase difference in radians is ?

Answer 1

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
maxdistance=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.