Question

When two displacements represented by $y_1 = a \sin \, (\omega \, t)$ and $y_2 = b \, cos \, ( \omega \, t )$ are superimposed the motion is

• A. simple harmonic with amplitude $\sqrt{ a^2 + b^2 }$
• B. simple harmonic with amplitude $\frac{ (a + b)}{ 2}$
• C. not a simple harmonic
• D. simple harmonic with amplitude $\frac{ a}{ b}$

Answer 1

Answer: (A)

simple harmonic with amplitude $\sqrt{ a^2 + b^2 }$

Answer 2

Here, $y_1 = a \, sin \, \omega t$
$y_2 = b \, cos \, \omega t = b \, sin \, \bigg( \omega t + \frac{ \pi}{ 2} \bigg)$

Hence, resultant motion is SHM with amplitude
$\sqrt{ a^2 + b^2 }$.