Simple Harmonic Motion and displacement

[IAmSparticus]

1. A 0.69 kg block is hung from and stretches a spring that is attached to the ceiling. A second block is attached to the first one, and the amount that the spring stretches from its unstrained length increases by a factor of 5. What is the mass of the second block?



2. Force= spring constant*displacement of spring from unstrained length



3. First off, I'm horrible at algebra so sorry if I make stupid mistakes in this attempt. The force is gravity so that becomes mg (.69kg*9.8 m/s/s).

mg=kx

If I pick a spring constant of 10 (does it matter what I pick?) then the equation becomes:

(.69kg)(9.8m/s/s)=10 x

Which would give a displacement of .6762 m. Now, when we increase it by a factor of 5, that displacement becomes 3.381 m. Plugging that into a new equations gives:

m (9.8m/s/s) = 10 (3.381m)

When I solve for m I get 3.45 kg, which is wrong. Someone tell me what I did wrong?

 

[Fightfish]

m is the total mass of the first and second blocks. Try to leave your work in symbols rather than substitute arbitrary numbers; its neater that way.

 

[IAmSparticus]

So if I leave it in the symbol format I get that (.69kg)(9.8m/s/s)=kx and m(9.8m/s/s)=k(5x). Now what?

 

[Fightfish]

(m1 + m2)g = 5 (kx) = 5 (m1)g
:. m2 = 4 m1