A) \[x=10.25\sin (\omega t+\phi )\]
B) \[x=10.25\sin (\omega t-\phi )\]
C) \[x=11.25\sin (\omega t+\phi )\]
D) \[x=11.25\sin (\omega t-\phi )\]
Correct Answer: C
Solution :
The resultant equation is \[x=A\sin (\omega t+\phi )\] \[\sum{{{A}_{x}}}=2+4\cos {{30}^{\circ }}+6\cos {{60}^{\circ }}=8.46\] and \[\sum{{{A}_{y}}=4\sin {{30}^{\circ }}+6\cos {{30}^{\circ }}=7.2}\] \[\therefore \] \[A=\sqrt{{{\left( \sum{{{A}_{x}}} \right)}^{2}}+{{\left( \sum{{{A}_{y}}} \right)}^{2}}}\] \[=\sqrt{{{(8.46)}^{2}}+{{(7.2)}^{2}}}=11.25\] and \[\tan \phi =\frac{\sum{{{A}_{y}}}}{\sum{{{A}_{x}}}}=\frac{7.2}{8.46}=0.85\] \[\Rightarrow \] \[\phi ={{\tan }^{-1}}(0.85)={{40.4}^{\circ }}\] Thus, the displacement equation of combined motion is \[x=11.25\sin (\omega t+\phi )\] where, \[\phi ={{40.4}^{\circ }}\]You need to login to perform this action.
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