The displacement of a particle varies with time according to the relation x = a t + b t

Step-by-step solution

Given displacement is x = a t + b t Multiplying and dividing by a^2 + b^2 , we get 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 x = a^2 + b^2 ( t + t ) x = a^2 + b^2 ( t + ) This represents a simple harmonic motion with amplitude A = a^2 + b^2 . Answer: The motion is simple harmonic motion with an amplitude a^2 + b^2