A particle is free to move on X-axis, in which of the following case, the particle will execute oscillation about x = 1?
A. F=(x-1)
B. F=-(x-1)^2
C. F=-(x-1)^3
D. F=F=(x-1)^3
Answers
(A) We have , F = (x-1)
•) Now, we have to find the motion of the particle on which this force is acting.
Now , for F = (x-1)
•) If x = 1 . F = 0
•) If x > 1 , F will be positive
•) If x < 1 , F will be negative
Now also equation of Simple Harmonic Motion is F = -kx
•) Hence , motion of the particle is Simple Hamonic Motion
(B) We have , F = -(x-1)^2
•) Now, we have to find the motion of the particle on which this force is acting.
Now , for F = -(x-1)^2
•) If x = 1 , F = 0
•) If x > 1 , F will be negative
•) If x < 1 , F will be negative
•) Hence , motion of the particle will be rectilinear
(C) We have , F = - (x-1)^3
•) Now, we have to find the motion of the particle on which this force is acting .
Now , for F = -(x-1)^3
•) If x = 1 , F = 0
•) If x > 1 , F will be negative
•) If x < 1 , F will be positive
•) Hence , motion of the particle will be Oscillatory around the point x = 1, but particle will be not be in Simple Harmonic Oscillation .
(D) We have , F = (x-1)^3
•) Now, we have to find the motion of the particle on which this force is acting .
Now , for F = (x-1)^3
•) If x = 1 , F = 0
•) If x > 1 , F will be positive
•) If x < 1 , F will be negative
•) Hence , motion of the particle will be Oscillatory around the point x = 1, but particle will be not be in Simple Harmonic Oscillation .