A particle in S.H.M. is described by the displacement function $$x(t)=acos($$ω$$t+$$θ$$)$$ . If the initial (t=0) position of the particle is $$1$$ cm and its initial velocity is π cm$$/$$s . The angular frequency of the particle is π $$rad/s$$, then it’s amplitude is

Question

A particle in S.H.M. is described by the displacement function $$x(t)=acos($$ω$$t+$$θ$$)$$ . If the initial (t=0) position of the particle is $$1$$ cm and its initial velocity is π cm​$$/$$​s . The angular frequency of the particle is π $$rad/s$$, then it’s amplitude is

Infinity Learn · Accepted Answer

$$x=acos($$ω $$t+$$θ$$)$$                                  ….(i)and$$  $$v=dxdt=$$−aω$$sin$$$$($$ω $$t+$$θ$$)          ….(ii)Given$$ at $$t=0$$, $$x=1$$ cm and  $$v=$$π and ω$$=$$πPutting these values in equation $$(i) and (ii) we will get $$sin$$θ$$=$$−$$1a$$ and  $$cos$$θ$$=1a$$⇒$$sin2$$θ$$+cos2$$θ$$=$$−$$1a2+1a2$$ ⇒$$a=2$$ cm

A particle in S.H.M. is described by the displacement function $x (t) = acos (ωt + θ)$ . If the initial $(t = 0)$ position of the particle is 1 cm and its initial velocity is $π cm / s$ . The angular frequency of the particle is $π rad / s$ , then it’s amplitude is

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A particle in S.H.M. is described by the displacement function x(t)=acos(ωt+θ) . If the initial (t=0) position of the particle is 1 cm and its initial velocity is π cm​/​s . The angular frequency of the particle is π rad/s, then it’s amplitude is

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Ready to Test Your Skills?

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A particle in S.H.M. is described by the displacement function $x (t) = acos (ωt + θ)$ . If the initial $(t = 0)$ position of the particle is 1 cm and its initial velocity is $π cm / s$ . The angular frequency of the particle is $π rad / s$ , then it’s amplitude is