Q7 of 111 Page 250

The motion of a particle is given by x = A sin ωt + B cos ωt. The motion of the particle is

As x given in the question satisfies the simple harmonic motion equation


∴ the above equation in question is a simple harmonic motion.


And can be represented as



Where , δ is the phase difference and .


And ,


In which can also be represented as,


∴ δ can be written as


And becomes


Hence, amplitude becomes.

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A particle moves on the X-ails according to the equation x = A + B sin ωt. The motion is simple harmonic with amplitude