# Spring problem

1. Feb 9, 2010

### sam12345

1. The problem statement, all variables and given/known data

A pair of masses M1, M2 is suspended vertically by a pair of spring, with spring constant k1, k2. ( see the attachment for the picture)

a.A downward force F is applied to bottom mass. Find the downward displacements d1 and d 2 of the equilibrium positions of the Mass M1and M2 due to the force. Note that effect of gravity is already taken into account in determing the equilibrium positions.

b.At time t =0, the downward force is removed. What are the equation of motion and initial conditions that determine the displacements d1(t) and d2(t) for t greater than 0? You need not solve the equations.

2. Relevant equations

m2g=k2x2
k2x2 + m2g+ m1g=k1x1
then i added them, I get 2m2g +m1g=k1x1

F=-kx

3. The attempt at a solution

m2g=k2x2
k2x2 + m2g+ m1g=k1x1
then i added them, I get 2m2g +m1g=k1x1.

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2. Feb 10, 2010

### sam12345

Btw, this is a Caltech problem!

3. Feb 10, 2010

### jhae2.718

For A, try creating separate free body diagrams for $m_1$ and $m_2$ and finding $\Sigma F_y=F_{app}$. Then, solve each for $d_1$ and $d_2$.

4. Feb 10, 2010

### Jebus_Chris

a) Both springs will experience force F. Since they are already in equilibrium you can "ignore" the masses.
$$F=k_1d_1$$
$$F=k_2d_2$$
b) Simple SHM equations.