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  • The displacement of the particle executing a simple harmonic motion is given by <img alt="Y= C 0+Csin \omega t+D cos \omega t" src="https://entrancecorner.oncodecogs.com/gif.latex?Y%3D%20C%200

The displacement of the particle executing a simple harmonic motion is given by Y= C 0+Csin \omega t+D cos \omega t . Then the amplitude of its oscillation is given by?

Option: 1

\begin{gathered} =\sqrt{c^2+D^2} \end{gathered}


Option: 2

\begin{gathered} =\sqrt{c^2+D} \end{gathered}


Option: 3

\begin{gathered} =\sqrt{c+D^2} \end{gathered}


Option: 4

None of these


Answers (1)

best_answer

\begin{gathered} Y=c 0+c \sin \omega t+D \cos \omega t \\ \text { or }(Y-c 0)=c \sin \omega t+D \cos \omega t \\ \text { or } Y^{\prime}=c \cos \left(\frac{\pi}{2}-\omega t\right)+D \cot \omega t \\ \text { Amplitude }=\sqrt{c^2+D^2+2 C D cos \frac{\pi}{2}} \quad\left[\because \varphi=\frac{\pi}{2}\right. \\ =\sqrt{c^2+D^2+2 C D \times 0} \\ =\sqrt{c^2+D^2} \end{gathered}

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