How Do You Determine the Amplitude of a Spring-Mass System?

[nrc_8706]

a block of mass 4kg is hung from a spring, causing it to stretch 8cm at equilibrium. the 4kg block is then replaced by a 5kg block. the accleration of gravity is 9.8m/s^2. how far will the 5kg block fall before its direction is reversed?


i don't know if this helps but i found K for the first block

F=-kx
4*9.8=.8k
k=49

i don't know anything else. HELP PLEASE

 

[durt]

8 cm is .08 m, not .8 m.
Just find the distance to the from the old equilibrium point to the new one (the amplitude of oscillation) and multiply by two.

 

[nrc_8706]

?

how do you find the amplitude?

 

[pseudovector]

Use the conservation of energy principal:
In the beggining of the motion, the spring is unstretched, so it has no energy whatsoever, but the mass has potential energy m*g*x, where x is the distance it will fall before coming to a halt.
In the end of the motion, the mass stops falling and is momentarily at rest, so it has neither potential nor kinetic energy. The spring, however, is now stretched by distance x from equilibrium, so the energy it has equals 0.5k*x^2. The energy at the beginning must be equal to the energy at the end, so you can write an equation and solve it to find x.