The motion of the particle is given by the equation x=A t+B t . The motion of the particle is

Step-by-step solution

The equation of motion x = A t + B t represents the superposition of two simple harmonic motions with identical angular frequency . This expression can be transformed into the standard simple harmonic form x = R ( t + ) by applying the trigonometric identity (X + Y) = X Y + X Y , yielding x = R t + R t . Matching coefficients with the original equation gives A = R and B = R . Squaring and adding these equations results in A^2 + B^2 = R^2 ^2 + R^2 ^2 = R^2( ^2 + ^2 ) = R^2 , since ^2 + ^2 = 1 . Therefore, the amplit