A particle is executing SHM in a straight line. Let x, v, and a represent instantaneous displacement, velocity and acceleration respectively. Graph of $$a2$$ vs $$v2$$ is

Question

A particle is executing SHM in a straight line. Let x, v, and a represent instantaneous  displacement, velocity and acceleration respectively. Graph of $$a2$$ vs $$v2$$ is

Infinity Learn · Accepted Answer

Displacement,    $$x=Asin$$ω$$t+$$ϕVelocity,     $$v=A$$ω$$cos$$ω$$t+$$ϕAcceleration,    $$a=$$−Aω$$2sin$$ω$$t+$$ϕ $$v=$$ω$$A2$$−$$x2$$⇒$$v2=$$ω$$2A2$$−$$x2$$   ...(1) $$a=$$−ω$$2x$$⇒$$a2=$$ω$$2x2$$     ...(2)(2) in (1) gives,So,  $$v2=$$ω$$2A2$$−$$a2$$ω$$4$$⇒$$v2A2$$ω$$2+a2A2$$ω$$4=1$$  It is of the form $$yK1+xK2=1$$ , where $$K1$$ and $$K2$$ are positive constants.   $$y=1K1$$−$$xK2K1$$⇒$$y=c$$−mx. It is a straight line with negative slope and positive  intercept.

A particle is executing SHM in a straight line. Let x, v, and a represent instantaneous displacement, velocity and acceleration respectively. Graph of a² vs v² is

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A particle is executing SHM in a straight line. Let x, v, and a represent instantaneous displacement, velocity and acceleration respectively. Graph of a2 vs v2 is

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A particle is executing SHM in a straight line. Let x, v, and a represent instantaneous displacement, velocity and acceleration respectively. Graph of a² vs v² is