A particle P of mass 2gms moves on the X-axis and is attracted towards origin O with a force numerically equal to 8x. If it is initially at rest at X = 10, find its position at any subsequent time assuming (a) no other force acts, (b) a damping force numerically equal to 8 times the instantaneous velocity act.

Answer 1

Since F=ma, a = 8x/m. So, we have

a(x) = -8/m x
v(x) = -4/m x^2 + c1
s(x) = -4/3 x^3 + c1*x + c2

v(0) = 0 and s(0) = 10, so
s(x) = -4/3 x^3 + 10

For the damping, just work with

v(x) = -4/m x^2 + 8v
and follow through to get s(x)

Answer 2

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