A particle executing SHM while moving from one extremity is found at distance $$x1$$, $$x2$$ and $$x3$$ from the centre at the end of three successive seconds. The time period of oscillation is (where$$ θ $$=$$ $$cos$$$$-1(x1+x32x2))

Question

A particle executing SHM while moving from one extremity is found at distance $$x1$$, $$x2$$ and $$x3$$ from the centre at the end of three successive seconds. The time period of oscillation is (where$$ θ $$=$$ $$cos$$$$-1(x1+x32x2))

Infinity Learn · Accepted Answer

$$Displacement-time$$ equation of the particle will beX $$=$$ A $$cos$$ ωtGiven that $$x1$$ $$=$$ A $$cos$$ ω and $$x2$$ $$=$$ A $$cos$$ $$2$$ωNow, $$x1+x32x2$$ $$=$$ $$A($$$$cos$$ θ$$+$$ $$cos$$ $$3$$ω$$)2Acos$$ $$2$$ω                        $$=$$ $$2$$ A $$cos$$ $$2$$ω $$cos$$ ω$$2A$$ $$cos$$ $$2$$ω                           $$=$$ $$cos$$ ωω $$=$$ $$cos$$$$-1(x1+x32x2)$$ $$=$$ $$2$$$$π$$Tor T $$=$$ $$2$$πθ where θ $$=$$ $$cos$$$$-1(x1+x32x2)$$

A particle executing SHM while moving from one extremity is found at distance $x_{1}, x_{2} and x_{3}$ from the centre at the end of three successive seconds. The time period of oscillation is (where $θ = \cos^{- 1} (\frac{x_{1} + x_{3}}{2 x_{2}})$ )

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A particle executing SHM while moving from one extremity is found at distance x1, x2 and x3 from the centre at the end of three successive seconds. The time period of oscillation is (where θ = cos-1(x1+x32x2))

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A particle executing SHM while moving from one extremity is found at distance $x_{1}, x_{2} and x_{3}$ from the centre at the end of three successive seconds. The time period of oscillation is (where $θ = \cos^{- 1} (\frac{x_{1} + x_{3}}{2 x_{2}})$ )