Question

Describe the motion of a particle acted upon by a force (i) F= -2(x - 2)^(3) (ii) F= -2(x - 2)^(2) (iii) F= -2(x - 2)

Answer 1

(i). We have , F = -2*(x-2)^3

•) Now, we have to find the motion of the particle on which this force is acting .

Now , for F = -2*(x-2)^3

•) If x = 2 , F = 0

•) If x > 2 , F will be negative

•) If x < 2 , F will be positive

•) Hence , motion of the particle will be oscillatory around the point x = 2 but particle will be not be in Simple Harmonic Oscillation .

(ii) We have , F = -2*(x-2)^2

•) Now, we have to find the motion of the particle on which this force is acting.

Now , for F = -2*(x-2)^2

•) If x = 2 , F = 0

•) If x > 2 , F will be negative

•) If x < 2 , F will be negative

•) Hence , motion of the particle will be rectilinear.

(iii) We have , F = -2*(x-2)

•) Now, we have to find the motion of the particle on which this force is acting.

Now , for F = -2*(x-2)

•) If x = 0 . F = 0

•) If x > 2 , F will be negative

•) If x < 2 , F will be positive

Now also equation of Simple Harmonic Motion is F = -kx

•) Hence , motion of the particle is Simple Hamonic Motion