A particle is moving with damped motion according to the law d2x/dt2 + 6dx/dt + 25x = 0. If the initial position of the particle is at x = 20 and the initial speed is 10, find the displacement of the particle at any time t using Laplace transforms
We have
x"(t) + 6x′(t) + 25x (t)=0
Initial conditions x (0) = 20, x′ (0) = 10
Taking Laplace transforms on both sides,
we get L [x"(t)] + 6L [x′ (t)] + 25L [x (t)] = L (0)
