Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The function f(t) = ( t) + (2 t) represents a periodic motion but not a simple harmonic motion. Reason (R): The given function can be reduced to a single sine function of the form A ( ' t + ) . In the light of the above statements, choose the most appropriate answer from the options given below:

Step-by-step solution

Assertion (A) is true: The function f(t) = ( t) + (2 t) is a superposition of two simple harmonic motions with angular frequencies and 2 . Since the ratio of their frequencies is a rational number, their sum repeats after a definite time interval and is therefore periodic. However, because the frequencies are different, the resulting motion is not a simple harmonic motion. Reason (R) is false: A function represents simple harmonic motion only if it can be expressed as a single sine or cosine function, such as A ( '