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When two displacements represented by $y_1 = a\sin(\omega t)$ and $y_2 = b\cos(\omega t)$ are superimposed the motion is
A
Not a simple harmonic
B
Simple harmonic with amplitude $\frac{a}{b}$
C
Simple harmonic with amplitude $\sqrt{a^2 + b^2}$
D
Simple harmonic with amplitude $\frac{(a+b)}{2}$
Detailed Solution
$y_2 = b\cos\omega t = b\sin\left(\omega t + \frac{\pi}{2}\right)$
Both SHMs have the same frequency, so the resultant motion is also SHM.
$A = \sqrt{a^2 + b^2 + 2ab\cos\phi}$ with $\phi = \frac{\pi}{2}$
$A = \sqrt{a^2 + b^2}$
Both SHMs have the same frequency, so the resultant motion is also SHM.
$A = \sqrt{a^2 + b^2 + 2ab\cos\phi}$ with $\phi = \frac{\pi}{2}$
$A = \sqrt{a^2 + b^2}$