A spring is stretched $175$ mm by a $10$ kg block. If the block is displaced $100$ mm downward from its equilibrium position and given a downward velocity of $1\mathrm{.}50$m$/$s$,$ determine the differential equation which describes the motion. Assume that positive displacement is downward. Determine the position of the block when t$=0\mathrm{.}22$ seconds. Plot the motion equation and discuss its meaning in the "think" section.

What is the known information?

Name each variable used and provide units. For example, force in cable AB$,$ F$\_($AB$)=$##$[$N$]$

What do you need to find?

Name each variable used and provide units. For example, force in cable AB$,$ FAB $=$ ## $[$N$]$

Engineering Model, Assumptions, Theory

State any assumptions that you are making. List any governing equations that are used in the solution

of the problem

Schematic$/$Diagram

Construct any diagrams that you will use to solve the problem. Be sure to label all points, include

units. Include a reference frame if relevant. Use the same variables that were used in the known, find,

and analysis sections. $($Note: you may need to construct more diagrams along the way $...$ that's ok$.$

I'll count all diagrams for this portion when grading. No need to re$-$draw.$)$

Analysis$/$Calculations

Perform the calculations necessary to solve the problem. Start from the base governing equation. Solve

symbolically as far as possible before substituting numerical values. Include any Table numbers used as

reference. Annotate your solution as much as possible to better understand your calculations. Use the

same variables that were used in the known and find sections. It may be necessary to include

additional diagrams as you progress through your solution.

Final Answers$/$Think

Report final answers and include units. Explain why the answer that you found makes sense $($or doesn't$).$

Think of an order of magnitude comparison, unit analysis, best$/$worst case comparisons, etc.