I have a system of a point mass m connected to a base with one spring and one damper in parallel. There is 0 gravity, 0 air resistance. The base has a constant acceleration towards the point mass m which of course is free to move away from the the base. Speed at time 0 is 0 for both objects. Inertia of the point mass is I guess the only thing allowing the base to get closer than initial distance.
I do not need to plot continuous curve, but I need to know the relative change in position between the base and the point mass at a given time.
m=100kg
damper coefficient c=variable
spring constant k=variable
constant acceleration a= 6g= 6x9.81m/s^2
time = 0.25s
my formula looks something like this
mx''+ cx' + kx = c*a*t + 1/2*k*a*t2
My particulate solution looks something like this: Xp(t)=1/2*a*t2 - m*a/k
This is pretty much as far as I have come. I do have a homogenous solution also, but it depends greatly on the value of k and c as you do know.
Could anyone help me to assess this?
I do not need to plot continuous curve, but I need to know the relative change in position between the base and the point mass at a given time.
m=100kg
damper coefficient c=variable
spring constant k=variable
constant acceleration a= 6g= 6x9.81m/s^2
time = 0.25s
my formula looks something like this
mx''+ cx' + kx = c*a*t + 1/2*k*a*t2
My particulate solution looks something like this: Xp(t)=1/2*a*t2 - m*a/k
This is pretty much as far as I have come. I do have a homogenous solution also, but it depends greatly on the value of k and c as you do know.
Could anyone help me to assess this?