Question

Two particles execute SHM of same amplitude of 20cm with same period along the same line about the same equilibrium position. The maximum distance between the two is 20cm. 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 

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.

Answer 2

we can use phasors or trignometric identities to solve this