The equation of the resulting oscillation obtained by the summation of two mutually perpendicular oscillations with the same frequency $$f1$$ $$=$$ $$f2$$ $$=$$ $$5$$ Hz and same initial phase δ$$1$$ $$=$$ δ$$2$$ $$=$$ $$600$$ is, $$(Given$$, their amplitudes are $$A1$$ $$=$$ $$0.1$$ m and $$A2$$ $$=$$ $$0.05$$ m

Question

The equation of the resulting oscillation obtained by the summation of two mutually perpendicular oscillations with the same frequency $$f1$$ $$=$$ $$f2$$ $$=$$ $$5$$ Hz and same initial phase δ$$1$$ $$=$$ δ$$2$$ $$=$$ $$600$$ is, $$(Given$$, their amplitudes are $$A1$$ $$=$$ $$0.1$$ m and $$A2$$ $$=$$ $$0.05$$ m

Infinity Learn · Accepted Answer

When x $$=$$ $$A1sin($$ωt $$+$$ ∅$$1)$$ and y $$=$$ $$A2$$ $$sin$$$$($$ω$$t+$$∅$$2)$$ $$thenx2A12+y2A22-2xyA1A2cos$$δ $$=$$  $$sin2$$δHere phase difference i.e., δ $$=$$ $$0$$∴  $$x2A21+y2A22-2xyA1A2$$ $$=$$ $$0$$⇒(xA1-yA2)2$$ $$=$$ $$0$$ ⇒y $$=$$ $$A2A1xResultant$$ amplitude isA $$=$$ $$A21+A22$$ $$=$$ $$(0.1)2+(0.05)2$$ $$=$$ $$0.112$$ mω $$=$$ $$2$$$$π$$$$f1$$ $$=$$ $$2$$$$π$$$$f2$$ $$=$$ $$10$$$$π$$Thus the equation of resulting SHM isr $$=$$ $$0.112$$ $$sin$$$$(10$$$$π$$$$t+$$π$$3)

The equation of the resulting oscillation obtained by the summation of two mutually perpendicular oscillations with the same frequency $f_{1} = f_{2} = 5 Hz$ and same initial phase $δ_{1} = δ_{2} = 60^{0}$ is, (Given, their amplitudes are $A_{1} = 0.1 m and A_{2} = 0.05 m$

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The equation of the resulting oscillation obtained by the summation of two mutually perpendicular oscillations with the same frequency f1 = f2 = 5 Hz and same initial phase δ1 = δ2 = 600 is, (Given, their amplitudes are A1 = 0.1 m and A2 = 0.05 m

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The equation of the resulting oscillation obtained by the summation of two mutually perpendicular oscillations with the same frequency $f_{1} = f_{2} = 5 Hz$ and same initial phase $δ_{1} = δ_{2} = 60^{0}$ is, (Given, their amplitudes are $A_{1} = 0.1 m and A_{2} = 0.05 m$