Working with two springs placed in series.
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
a 3-lb block can slide without friction in a slot and is connected to two springs of constant k_1=80 lb/ft and k_2=6 lb/ft. The springs are initially unstreatched when the block is pulled 2 in. to the right and released.Determine (a) the maximum velocity of the block, (b)the velocity of the block when it is 0.8 in. from its initial position.
See attached for diagram.© BrainMass Inc. brainmass.com May 24, 2023, 1:13 pm ad1c9bdddf
Please see the attached file.
Consider two springs placed in series with a mass on the bottom of the second. The force is the same on each of the two springs. Therefore
Solving for in terms of ,
We are looking for the effective spring constant so that
Where is the total displacement of the mass. Equating (3) with the right side of (1) and ...
The solution gives all steps along with proper explanations so that you can solve similar problems yourself. All mathematical steps are clearly shown.