A particle in S.H.M. is described by the displacement function $$x(t)$$ $$=$$ a $$cos$$ $$($$ωt $$+$$ θ$$)$$.If the initial (t$$ $$=$$ $$0) position of the particle is I cm and its initial velocity is π $$cm/s$$. The angular frequency of the particle is π $$rad/s$$, then its amplitude is

Question

A particle in S.H.M. is described by the displacement function $$x(t)$$ $$=$$ a $$cos$$ $$($$ωt $$+$$ θ$$)$$.If the initial (t$$ $$=$$ $$0) position of the particle is I cm and its initial velocity is π $$cm/s$$. The angular frequency of the particle is π $$rad/s$$, then its amplitude is

Infinity Learn · Accepted Answer

x $$=$$ a $$cos$$ $$($$ωt $$+$$ θ$$)------------(i)And$$ v $$=$$ dxdt $$=$$ $$-a$$ω $$sin$$$$($$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 getsin θ $$=$$ $$-1a$$ and $$cos$$ θ $$=$$ $$1A$$⇒ $$sin2$$θ $$+$$ $$cos2$$θ $$=$$ $$(-1a)2+(1a)2$$  ⇒ a $$=$$ $$2$$ cm

A particle in S.H.M. is described by the displacement function x(t) = a cos ( $ωt + θ$ ).If the initial (t = 0) position of the particle is I cm and its initial velocity is $π cm / s$ . The angular frequency of the particle is $π rad / s$ , then its amplitude is

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A particle in S.H.M. is described by the displacement function x(t) = a cos (ωt + θ).If the initial (t = 0) position of the particle is I cm and its initial velocity is π cm/s. The angular frequency of the particle is π rad/s, then its amplitude is

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A particle in S.H.M. is described by the displacement function x(t) = a cos ( $ωt + θ$ ).If the initial (t = 0) position of the particle is I cm and its initial velocity is $π cm / s$ . The angular frequency of the particle is $π rad / s$ , then its amplitude is