A particle of mass 2 kg moves along the x-axis attracted toward the origin by a force whose magnitude is 8x. If the mass is initially at rest at x = 20, find the following:

Question

A particle of mass 2 kg moves along the x-axis attracted toward the origin by a force whose magnitude is 8x. If the mass is initially at rest at x = 20, find the following:

a) The differential equation and initial conditions describing the motion.
b) The position of the particle at any time.
c) The velocity of the particle at any time.
d) The amplitude, period and frequency of the motion.

Answer 1

F = ma, so

x"(t) = -4x
x(0) = 20

x = 20 cos(2t)

now finish it off