Comparative study of displacement, velocity, and acceleration in SHM
Displacement, y = a sin Ï‰t
Velocity,
Acceleration, A = â€“aÏ‰^{2} sin Ï‰t = aÏ‰^{2} sin (Ï‰t + Ï€)
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 Ï‰ times the displacement amplitude
 The acceleration amplitude is Ï‰^{2} times the displacement amplitude
 In SHM the velocity is ahead of displacement by a phase angle Ï€ /2
 In SHM the acceleration is ahead of velocity by a phase angle Ï€ /2
 The acceleration is ahead of displacement by a phase angle of Ï€
 Various physical quantities in SHM at different position:
Physical quantities

Equilibrium position (y= 0)

Extreme position (y = Â± a)

Displacement y= a sin Ï‰t

Minimum (Zero)

Maximum (a)

Velocity

Maximum (aÏ‰)

Minimum (Zero)

Acceleration

Minimum (Zero)

Maximum (Ï‰^{2} a)
