Solve for y in terms of t

(d^2 * y)/(d * t^2) + 6 * (dy/dt) + 9y = 0 y(0) = 10, y'(0) = 0

Solve for y in terms of t

(d^2 *y)/(d*t^2) + 3*(dy/dt) + 2y = 24* exp(-4*t), y(0)=10, y'(0)=5

Laplace Transform

Find the inverse Laplace transform of (s^3+s^2+2/s) / [s^2(s^2+3s+2)] Using this (or otherwise), Find the solution of the equation y"+3y'+2y = 1-t Find the transform of the following functions: f(t) = (1+t^2)[u(t-1)-u(t-2)] where u(t) is the unit step function. f(t) = sin(t) for 0

Linear system

Please see attachment.

This question is about an underdamped harmonic oscillator.

Suppose a suspension system of the average car can be fairly well modeled by an inderdamped harmonice oscillator with a natural period of 2 seconds. How far apart should speed bumps be placed so that a car traveling 10 mph over several bumps will bounce more and more violently with each bump?