A particle executes simple harmonic motion and is located at $$x=a$$,b and c at times to,$$3to$$ and $$5to$$ respectively with respect to mean position . At $$t=0$$, the particle is at the mean position and moving toward positive $$x-axis$$. The frequency of the oscillation is

Question

A particle executes simple harmonic motion and is located at  $$x=a$$,b and  c at times to,$$3to$$ and $$5to$$ respectively with respect to mean position . At  $$t=0$$, the particle is at the mean position and moving toward positive $$x-axis$$. The frequency of the oscillation is

Infinity Learn · Accepted Answer

Using $$y=Asin$$⁡ω$$ta=Asin$$⁡ω$$t0b=Asin$$⁡$$3$$ω$$t0c=Asin$$⁡$$5$$ω$$t0a+c=Asin$$⁡ω$$t0+Asin$$⁡$$5$$ω$$t0=2Asin$$⁡$$3$$ω$$t0cos$$⁡$$2$$ω$$t0=2bcos$$⁡$$2$$ω$$t0$$⇒$$a+cb=2cos$$⁡$$2$$ω$$t0$$⇒$$a+c2b=$$$$cos$$⁡$$2$$ω$$t0$$⇒ω$$=12t0cos$$−$$1$$⁡$$a+c2b($$∵ω$$=2$$$$π$$$$f)$$⇒$$f=14$$$$π$$$$t0$$×$$cos$$−$$1$$⁡$$a+c2bTherefore$$, the correct answer is (C).

A particle executes simple harmonic motion and is located at $x = a, b$ and $c$ at times $t_{o}, 3 t_{o}$ and $5 t_{o}$ respectively with respect to mean position . At $t = 0$ , the particle is at the mean position and moving toward positive x-axis. The frequency of the oscillation is

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A particle executes simple harmonic motion and is located at x=a,b and c at times to,3to and 5to respectively with respect to mean position . At t=0, the particle is at the mean position and moving toward positive x-axis. The frequency of the oscillation is

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A particle executes simple harmonic motion and is located at $x = a, b$ and $c$ at times $t_{o}, 3 t_{o}$ and $5 t_{o}$ respectively with respect to mean position . At $t = 0$ , the particle is at the mean position and moving toward positive x-axis. The frequency of the oscillation is