Question

In SHM, which equation represent general equation, equation from mean position, equation from extreme position respectively.

$\left(P\right)y=A\sin (wt+\alpha )$

$\left(Q\right)y=A\sin \left(wt\right)$

$\left(R\right)y=A\cos \left(wt\right)$

$A.R,Q,P$

$B.P,R,Q$

$C.P,Q,R$

$D.Q,R,P$

Answer 1

$Thecorrectanswerisoption\left(C\right)$

$solution:$

$AsweknowinSHM,displacementequationy=A\sin \left(wt\right),ifweputt=0,$

$weshouldgety=0,$

$thereforewecansayparticlemusthavestarteditsjourneyatt=0fromorigin.$

$Hence,y=A\sin \left(wt\right)representsequationofSHMfrommeanposition.$

$ForExtremeposition,Asparticlereachesextremeposition,itgoesbythe{90}^{0}phase.$

$\therefore y=A\sin (wt+\frac{\pi }{2})$

$\therefore y=A\cos \left(wt\right),representsequationofSHMfromextremeposition.$

$forGeneralSHMequation,particlemusthavestartedfromanywherebetween$

$extremeandmeanposition.\left(excludingmeanandextremeposition\right)$

$\therefore y=A\sin (wt+\alpha )$