Rankers Physics

Equation of SHM: Practice Problem & Solution

When two displacements represented by $ y_1 = a \sin(\omega t) $ and $ y_2 = b \cos(\omega t) $ are superimposed, the motion is: (2015)
Simple harmonic with amplitude $ \frac{a}{b} $
Simple harmonic with amplitude $ \sqrt{a^2 + b^2} $
Simple harmonic with amplitude $ \frac{(a+b)}{2} $
Not a simple harmonic

Solution Explained:

To solve this problem, we apply the core principles of Equation of SHM. Understanding the underlying formula is key to arriving at the correct answer below:

The resultant displacement is $ y = y_1 + y_2 = a \sin(\omega t) + b \cos(\omega t) $. This equation represents a single simple harmonic motion with a resultant amplitude of $ R = \sqrt{a^2 + b^2} $.

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