Question

The equation of an SHM with amplitude A and angular frequency ω in which all the distances are measured from one extreme position and time is taken to be zero at the other extreme position is
(1) x = A sin ωt
(2) x = A (cos ωt + sin ωt)
(3) x = A – A cos ωt
(4) x = A + A cos ωt

Answer 1

Dear student
$$\begin{gathered} Letthetimeismeasuredwhentheparticleisatitspositiveextremepositionanddis\tan ceismeasuredfromthenegativeextremepositionofSHM. \\ Letpositionofparticlebe \\ x=A\sin (\omega t+\theta ) \\ att=0particleislyingthatisx=+Aatitsnegativeextremeposition \\ A=A\sin (\omega \times 0+\theta ) \\ \sin \theta =1 \\ \theta =\frac{\pi }{2} \\ x=A\sin (\omega t+\frac{\pi }{2})=A\cos \left(\omega t\right) \\ Dis\tan ceofparticlefromthemeanpositionattimetisx=A\cos \left(\omega t\right) \\ Sodis\tan ceofparticlefromnegativeextremepositionis \\ X=A+x=A+A\cos \left(\omega t\right) \\ Regards \end{gathered}$$