A particle of mass m is attached to a spring (of$$ spring constant $$k) and has a natural angular frequency ω$$0$$. . An external force $$F(f)$$ proportional to $$cos$$ ωtω≠ω$$0is$$ applied to the oscillator. The time displacement of the oscillator will be proportional to

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A particle of mass m is attached to a spring (of$$ spring constant $$k) and has a natural angular frequency ω$$0$$. . An external force $$F(f)$$ proportional to $$cos$$ ωtω≠ω$$0is$$ applied to the oscillator. The time displacement of the oscillator will be proportional to

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Given that natural angular frequency $$=$$ω$$0$$ Let at any instant t, angular frequency $$=$$ω At a displacement x, the resultant $$accelerationf=$$ω$$02$$−ω$$2x$$ External forec. $$F=m$$ω$$02$$−ω$$2x$$ Given that F∝$$cos$$⁡$$($$ω$$t)$$ ∴ mω$$02$$−ω$$2x$$∝$$cos$$⁡$$($$ω$$t)$$  We know that $$x=Asin$$⁡$$($$ω$$t+$$ϕ$$)$$ Where the symbols have their usual meanings' Now $$A=Asin$$⁡(0+$$ϕ$$) $$($$∵ at $$t=0$$,$$x=A)$$ ∴ ϕ$$=$$π$$/2$$ thererefore $$x=Asin$$⁡ω$$t+$$π$$2=Acos$$⁡ωt From eqs. (3) and [$$5)$$, we gst mω$$02$$−ω$$2Acos$$⁡ωt∝$$cos$$⁡ωt or A∝$$1m$$ω$$02$$−ω$$2$$

A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency $ω_{0} .$ . An external force F(f) proportional to cos $ωt (ω \neq ω_{0})$ is applied to the oscillator. The time displacement of the oscillator will be proportional to

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A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ω0. . An external force F(f) proportional to cos ωtω≠ω0is applied to the oscillator. The time displacement of the oscillator will be proportional to

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A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency $ω_{0} .$ . An external force F(f) proportional to cos $ωt (ω \neq ω_{0})$ is applied to the oscillator. The time displacement of the oscillator will be proportional to