# Solve for position given force in a mass-spring system?

• kal854
In summary, the conversation is about determining the equations of motion for a mass attached to two springs in a system, starting from rest and with one spring extended by the weight of the mass. The hint is to use FBDs and equations for forces and distances, and to plot the force in the springs over time for different values of alpha. The speaker was asked to provide their work toward a solution before receiving help.

#### kal854

Picture of the system (it's sideways): http://tinypic.com/r/28qq4pi/5

Consider the mass from the spring in the figure. Let m=1, k=1, and g=9.81. Assume that x and y are zero when the 2 springs are unstretched. Assume the system starts from rest with the first spring extended by an amount equal to the weight of the mass and the second spring is unstretched.

Determine the equations of motion for x and y. Let F=(alpha)*t and solve for x(t) and y(t) for various values of alpha. Plot the force in the spring vs. time for different values of alpha.

Hint: the force in the top spring is kx, and the force in the bottom spring is k(y-x).

Thanks in advance for any of your input! I have no idea where to start.

Try taking both blocks and make them into separate FBD and write equations for both of them and see where that gets you. You should be able to get multiple equations relating the forces and distances for each.

EDIT: Sorry, thought there were two blocks. Draw a FBD for the one block and write out all the forces acting on it as a function of x and y.

Last edited:
kal854 said:
Picture of the system (it's sideways): http://tinypic.com/r/28qq4pi/5

Consider the mass from the spring in the figure. Let m=1, k=1, and g=9.81. Assume that x and y are zero when the 2 springs are unstretched. Assume the system starts from rest with the first spring extended by an amount equal to the weight of the mass and the second spring is unstretched.

Determine the equations of motion for x and y. Let F=(alpha)*t and solve for x(t) and y(t) for various values of alpha. Plot the force in the spring vs. time for different values of alpha.

Hint: the force in the top spring is kx, and the force in the bottom spring is k(y-x).

Thanks in advance for any of your input! I have no idea where to start.

Please check your PMs. You are required to show your work toward a solution before we can offer tutorial help. Just saying that you "have no idea where to start" is not acceptable here on the PF.