Help on a Physics problem.. kind of confused on how to do this one..?

Question

A platform of mass 0.8 kg is supported on four springs (only two springs are shown in the picture, but there are four altogether). A chunk of modeling clay of mass 0.6 kg is held above the table and dropped so that it hits the table with a speed of v = 0.9 m/s.

The clay sticks to the table so that the the table and clay oscillate up and down together. Finally, the table comes to rest 6 cm below its original position.

a) What is the effective spring constant of all four springs taken together?

b) With what amplitude does the platform oscillate immediately after the clay hits the platform?

Answer 1

Since we know the final equilibrium of the table with the clay stuck on top we know that
k*x1=.8*g
and
k*x2=1.4*g
and
k*(x1-x2)=.6*g
and
x1-x2=6 cm
or 6/100 m
so
k=100*.6/6 * g
or
k=10*g

To find the amplitude look at the speed of the platform after impact using conservation of momentum
.6*.9=1.4*vf
vf=.6*.9/1.4

now using conservation of energy post collision
.5*1.4*vf^2-.5*k*x^2+1.4*g*x=0 is the equation of range of the platform. Solve for the two roots and you'll have the amplitude of oscillation.

j

Answer 2

a) 1/4

Answer 3

wow...so THIS Is how I barely passed Physics, now I remember! haha. Good luck!