Question

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

Answer 1

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.