A particle's motion is described by the equation x = A t + B t . The motion of this particle is

Step-by-step solution

Given equation of motion is x = A t + B t . Multiplying and dividing the right side by A^2 + B^2 : x = A^2 + B^2 ( A A^2 + B^2 t + B A^2 + B^2 t ) Let = A A^2 + B^2 and = B A^2 + B^2 . Substituting these values, we get: x = A^2 + B^2 ( t + t ) x = A^2 + B^2 ( t + ) This represents simple harmonic motion with an amplitude of A^2 + B^2 .