Question 55: Oscillations

Question

A particle is subjected to two simple harmonic motions as :

$$
x_1=\sqrt{7} \sin 5 \mathrm{tcm}
$$

and $x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}ight) \mathrm{cm}$
where $x$ is displacement and $t$ is time in seconds.
The maximum acceleration of the particle is $x 	imes 10^{-2} \mathrm{~ms}^{-2}$. The value of $x$ is :

Accepted Answer

$$\begin{aligned}
&\begin{aligned}
& x_1=\sqrt{7} \sin 5 t \
& x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}ight)
\end{aligned}\
&	ext { From phasor, }
\end{aligned}$$
$$\begin{aligned}
&	herefore 	ext { Amplitude of resultant } \mathrm{SHM}=7\
&\begin{aligned}
& \phi=	an ^{-1} \frac{2 \sqrt{7} 	imes \sqrt{3} / 2}{\sqrt{7}+2 \sqrt{7} 	imes \frac{1}{2}}=	an ^{-1} \frac{\sqrt{21}}{2 \sqrt{7}}=	an ^{-1} \frac{\sqrt{3}}{2} \
& 	herefore X_R=7 \sin (5 \mathrm{t}+\phi) \
& \quad a_R=-7 	imes 25 \sin (5 \mathrm{t}+\phi) \
& 	herefore a_{\max }=175 \mathrm{~cm} / \mathrm{sec}=175 	imes 10^{-2} \mathrm{~m} / \mathrm{sec}
\end{aligned}
\end{aligned}$$

Answer

$5 \sqrt{7}$

Answer

125

Answer

$25 \sqrt{7}$

Answer

175

Oscillations

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