1.A mass weighing 20 N is tied a spring hanging from the ceiling, and stretches the

spring 5 m. The damping force is numerically equal to 6 times the instantaneous velocity, at

all times. Suppose the mass is set in motion by compressing the spring 2m, and releasing it

with no initial velocity. Use g = 10 m=s2 for gravitational acceleration.

a) Write the ODE with initial conditions modelling the position of the mass at any time t (you

may assume t 0).

b) Solve the ODE from part a

c) How high up does the mass ever get?

d) Which direction is the mass traveling the first time it passes through the equilibrium position?

2.Solve the IVP using Laplace transforms

y"+9y=u(t-2) y(0)=0, y'(0)=1

3.Solve the IVP using Laplace transforms

y"-4y=(t-1) y(0)=0, y'(0)=0