Two SHM's x₁ = a ( t + 3 2 ) and x₂ = a ( t + ) are superimposed on each other. The resultant amplitude of motion is ( /2 = 1 and /2 = 0)

Step-by-step solution

Given equations of SHM are x₁ = a ( t + 3 2 ) and x₂ = a ( t + ) . The phase difference between the two SHMs is = 3 2 - = 2 . The resultant amplitude A is given by A = a₁^2 + a₂^2 + 2a₁a₂ ( ) . Substituting a₁ = a , a₂ = a , and = 2 : A = a^2 + a^2 + 2a^2 ( 2 ) Since ( 2 ) = 0 , we get: A = 2a^2 = a 2 Answer: a 2