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Comparative study of displacement, velocity, and acceleration in SHM

Displacement, y = a sin ωt
Velocity, 60309.png
Acceleration, A = –2 sin ωt = 2 sin (ωt + π)
Fig. 1
From the above equations and Fig. 1, we can conclude that:
  • All the three quantities displacement, velocity, and acceleration show harmonic variation with time having same period.
  • The velocity amplitude is ω times the displacement amplitude
  • The acceleration amplitude is ω2 times the displacement amplitude
  • In SHM the velocity is ahead of displacement by a phase angle π /2
  • In SHM the acceleration is ahead of velocity by a phase angle π /2
  • The acceleration is ahead of displacement by a phase angle of π
  • Various physical quantities in SHM at different position:
Physical quantities
Equilibrium position (y= 0)
Extreme position (y = ± a)
Displacement ya sin ωt
Minimum (Zero)
Maximum (a)
Velocity 60294.png 
Maximum ()
Minimum (Zero)
Acceleration 60287.png 
Minimum (Zero)
Maximum (ω2 a)

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