Question 213: Oscillations

Question

The motion of the particle is given by the equation $\mathrm{x}=\mathrm{A} \sin \omega \mathrm{t}+\mathrm{B} \cos \omega \mathrm{t}$.
The motion of the particle is

Accepted Answer

Motion of the particle is given by
$$ \begin{aligned} x=A \sin \omega t+B \cos \omega t & =A \sin \omega t+B \sin (\omega t  +\pi / 2) \end{aligned} $$
Resultant amplitude of a particle performing S.H.M. represented by the following equation is given by -
$$ \begin{aligned} \mathrm{R} & =\sqrt{\mathrm{A}_1^2+\mathrm{A}_2^2+2 \mathrm{~A}_1 \mathrm{~A}_2 \cos \left(\phi_1-\phi_2ight)} \ 	herefore \quad \mathrm{R} & =\sqrt{\mathrm{A}^2+\mathrm{B}^2} \quad \ldots .\left(\because \phi_1-\phi_2=-\frac{\pi}{2}ight) \end{aligned} $$

Answer

simple harmonic with amplitude $(\mathrm{A}+\mathrm{B})$

Answer

simple harmonic with amplitude $(A-B)$

Answer

simple harmonic with amplitude $\left(A^2+B^2\right)^{\frac{1}{2}}$

Answer

not simple harmonic

Oscillations

The motion of the particle is given by the equation \mathrm{x}=\mathrm{A} \sin \omega \mathrm{t}+\mathrm{B} \cos \omega \mathrm{t}. The motion of the particle is

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