Finding Displacement, Velocity, and Acceleration in a Viscously Damped System

[andrewport87]

Homework Statement

A viscously damped system has a total weight of 250 N, a spring stiffness k = 8 kN/m,
and a damping coefficient c = 0.08 kN-sec/m. Determine the displacement, velocity,
and acceleration of the mass as a function of time if it is disturbed from its equilibrium
position with an initial velocity of 0.25 m/sec with no initial displacement. Calculate
the displacement, velocity and acceleration of the mass at t = 1.75 sec.

Homework Equations

N?A

The Attempt at a Solution

I don't know where to start with this, i tried, x = ½( v + v0 )t
Where:
x = displacement
v = velocity
v0 = initial velocity

but the question doesn't give all the varibales needed, think I'm going about it the wrong way

 

[BruceW]

hi man, welcome to physicsforums!

You need to use an equation which takes into account the physics of the situation. Do you know what equation to use if it was just a mass on a spring? And have you learned about how the equation should change when the motion of the mass is damped? They do give enough information, as long as you know what the equation is.

 

[vela]

I don't know where to start with this, i tried, x = ½( v + v0 )t
Where:
x = displacement
v = velocity
v0 = initial velocity

but the question doesn't give all the variables needed, think I'm going about it the wrong way

That equation only works for situations involving constant acceleration.

As BruceW noted, you first need to identify the proper physics. The phrase "viscously damped system" is a clue. The fact that there's a spring, a mass, and a damping coefficient is another.

 

[andrewport87]

hi man, welcome to physicsforums!

You need to use an equation which takes into account the physics of the situation. Do you know what equation to use if it was just a mass on a spring? And have you learned about how the equation should change when the motion of the mass is damped? They do give enough information, as long as you know what the equation is.

To be honest, we got a crash course on the subject in 2 hours, then gave an assessment on it so we really haven't learned any of it and reading through the notes none of it makes sense. I'm a 4th year under graduate student and this is the first time I've ever done anything like this, its completely new, i don't even know the basics if I'm being completely honest, this has basically just been through at us and told to work through it.

only equation i can find for dampening force is:

Fd = cx

where x is the velocity and c is the coefficent and Fd is the dampening force, but again missing one of the variables, i think I'm missing something completely out

 

[vela]

Try looking up "damped harmonic oscillator." This is typically covered in freshman physics.