A particle executing SHM is described by the displacement function x(t)=Acos(omegat+phi), if the initial (t=0) position of the particle is 1 cm, its initial velocity is pi" cm "s^(-1) and its angular frequency is pis^(-1), then the amplitude of its motion is

A particle executing SHM is described by the displacement function x(t

1.	A particle executing SHM is described by the displacement function x(t)=Acos(omegat+phi), if the initial (t=0) position of the particle is 1 cm, its initial velocity is pi" cm "s^(-1) and its angular frequency is pis^(-1), then the amplitude of its motion is
Answer» `picm` 2 CM `sqrt(2)`cm 1 cm Solution :`x=Acos(omegat-phi)` where A is amplitude. At t=0, x=1 cm `therefore1=Acosphi`. . . (i) Velocity, `v=(dx)/(dt)=(d)/(dt)(aCos(omegat+phi))=-Aomegasin(omegat+phi)`. . . (II) SQUARING and adding (i) and (ii), we get `A^(2)cos^(2)phi+A^(2)sin^(2)phi=2` `A^(2)=2""(becausesin^(2)phi+cos^(2)phi=1)` `thereforeA=sqrt(2)cm`