# Give the graphical representation of , displacement, velocity, acceleration of a particle exucuting SHM mention the differences between them .

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X = displacement of a particle from its mean position

x = A Sin (w t + Ф)

T = 2 π / w

x = 0 at - Ф/w , T/2 - Ф/w , T - Ф/w , 1.5 T - Ф /w

x = A at T/4 - Ф /w , 5 T/4 - Ф/w, ....

x = - A at 3T/4 - Ф /w , 7 T/4 - Ф/w, ....

velocity = dx/dt = Aw Cos (wt + Ф)

v = 0 at T/4 - Ф/w, 5 T/4 - Ф/w , ...

v = A w at -Ф/w, T- Ф/w ,....

V = - A w at T/2 - Ф/w, 3T/2 - Ф/w ,...

acceleration = a dv/dt = - A w² Sin (w t + Ф)

a = 0 at - Ф/w , T/2 - Ф/w , T - Ф/w , 1.5 T - Ф /w

a = A w² at T/4 - Ф /w , 5 T/4 - Ф/w, ....

a - A w² at 3T/4 - Ф /w , 7 T/4 - Ф/w, ....

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__similarities __are that they have the same period.

__the differences among them is :__

Displacement and velocity differ by a phase of π/2. The phase of velocity is π/2 more than that of displacement.

Similarly, velocity and acceleration differ by a phase of π/2.

acceleration and displacement differ by a phase of π.

The peak amplitude of the displacement = A. fixed.

Amplitude of the velocity = A w => depends on the frequency.

Acceleration amplitude = A w² => also depends on the frequency.

x = A Sin (w t + Ф)

T = 2 π / w

x = 0 at - Ф/w , T/2 - Ф/w , T - Ф/w , 1.5 T - Ф /w

x = A at T/4 - Ф /w , 5 T/4 - Ф/w, ....

x = - A at 3T/4 - Ф /w , 7 T/4 - Ф/w, ....

velocity = dx/dt = Aw Cos (wt + Ф)

v = 0 at T/4 - Ф/w, 5 T/4 - Ф/w , ...

v = A w at -Ф/w, T- Ф/w ,....

V = - A w at T/2 - Ф/w, 3T/2 - Ф/w ,...

acceleration = a dv/dt = - A w² Sin (w t + Ф)

a = 0 at - Ф/w , T/2 - Ф/w , T - Ф/w , 1.5 T - Ф /w

a = A w² at T/4 - Ф /w , 5 T/4 - Ф/w, ....

a - A w² at 3T/4 - Ф /w , 7 T/4 - Ф/w, ....

=====================

Displacement and velocity differ by a phase of π/2. The phase of velocity is π/2 more than that of displacement.

Similarly, velocity and acceleration differ by a phase of π/2.

acceleration and displacement differ by a phase of π.

The peak amplitude of the displacement = A. fixed.

Amplitude of the velocity = A w => depends on the frequency.

Acceleration amplitude = A w² => also depends on the frequency.