A particle moves along the x-axis according to the law d2x/dt2 + 6 dx/dt + 25x = 0. If the particle is started at x = 0, with an initial velocity of 12 ft/sec to the left, determine x in terms of t using Laplace transform method
The given equation is
x"(t) + 6x′(t) + 25x(t) = 0 ...(1)
and x = 0 at t = 0, dx/dt = – 12 at t = 0, By data
i.e., x (0) = 0, x′ (0) = – 12 are the initial conditions.
Now taking Laplace transform on both sides of (1) we have
