Platform on Springs: Find Effective Spring Constant & Oscillation Amplitude

[confused1]

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?

 

[ColdFusion85]

Can you show us what work and/or ideas you have put forth so far?

 

[confused1]

a) What is the net displacement Delta x of the spring from its former equilibrium position? What force F was required to compress the springs? The effective spring constant is the ratio F/(delta x).

 

[OlderDan]

The first thing in this problem is a conservtion of momentum. Assume the collision is instantaneous, so there are no net forces to worry about. What will be the velocity of the clay/platform combination immediately after collision?