# JEE Main & Advanced Physics Simple Harmonic Motion Comparative Study of Displacement Velocity and Acceleration

Comparative Study of Displacement Velocity and Acceleration

Category : JEE Main & Advanced

(1) All the three quantities displacement, velocity and acceleration show harmonic variation with time having same period.

(2) The velocity amplitude is $\omega$ times the displacement amplitude

(3) The acceleration amplitude is ${{\omega }^{2}}$ times the displacement amplitude

(4) In S.H.M. the velocity is ahead of displacement by a phase angle $\pi /2$

(5) In S.H.M. the acceleration is ahead of velocity by a phase angle $\pi /2$

(6) The acceleration is ahead of displacement by a phase angle of $\pi$

Various physical quantities in S.H.M. at different position :

 Graph Formula At mean position At extreme position Displacement $y=a\sin \omega \,t$ $y=0$ $y=\pm a$ Velocity $v=a\omega \cos \omega \,t$ $=a\omega \sin (\omega \,t+\frac{\pi }{2})$ or $v=\omega \sqrt{{{a}^{2}}-{{y}^{2}}}$ ${{v}_{\max }}=a\omega$ ${{v}_{\min }}=0$ Acceleration $A=-a{{\omega }^{2}}\sin \omega \,t$ $=a{{\omega }^{2}}\sin (\omega \,t+\pi )$ or $\left| A\, \right|={{\omega }^{2}}y$ ${{A}_{\min }}=0$ $|{{A}_{\max }}|$ ${{\omega }^{2}}a$ Force $F=-\,m{{\omega }^{2}}a\sin \omega \,t$ or $F=m{{\omega }^{2}}y$ ${{F}_{\min }}=0$ ${{F}_{\max }}=$ $\,m{{\omega }^{2}}a$

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