Find the amplitude of the oscillation of the particle. > The displacement of a particle varies according to $x=3(\cos t +\sin t)$. Then find the amplitude of the oscillation of the particle. Can someone kindly explain the concept of amplitude and oscillation and how to solve it? Any hints for solving the problem would be helpful.

The amplitude of a particle is the largest distance it moves from the equilibrium point when moving periodically. Oscillation is just a word used to define movement which follows a regular pattern.

To find the amplitude of the oscillation of $x$ we need to find the maximum value of $3\cos{t}+3\sin{t}$ when $t$ varies. $$3\cos{t}+3\sin{t}=3\sqrt{2}\sin{(t+\frac{\pi}{4})}$$ So, the maximum value of the displacement - the amplitude of the particle - is $3\sqrt{2}$.