What do you mean by vibration, Mechanical Engineering

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A body is subjected to two harmonic motions as given below :

X₁ = 15 sin (wt + 30⁰) and X₂ = 8 cos (wt + 60⁰). What harmonic motion should be given to the body to bring it to equilibrium.

What is vibration and its need to study. Also give the importance of vibration.

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