# Mathematical Model

1. Jun 4, 2014

### ashclouded

The problem statement, all variables and given/known data[/b]
Develop a mathematical model that would lengthen the time until the shock stabilised by the given time. T= 2.51 show mathematical analysis of the situation

d(t) = -5e^(-5t) cos (10t) is the original equation for a deflection of a rod in centimetres where t is time and d is deflection.

once a rod is released at time 0, it will spring back towards rest position where deflection is 0. It will go past rest which is called first rebound before rebounding again, going back through rest. the maximum distance of the rod below the rest position after this first rebound (dm) is used to measure the perfomance of the damper. dividing this rebound distance by the initial displacement (which is 5cm) gives the rebound ratio for that particular damper. if the ratio is below 1% the damper is working correctly.
I found from the graph that the given function of deflection stabilises around pi/3 but I don't think that's how I'm supposed to do the question

2. Jun 5, 2014

### LCKurtz

Why don't you tell us what it means for a shock to be "stabilized by the given time"?

Once you explain what you are trying to do and show us what calculations you did, perhaps we can help you.

3. Jun 5, 2014

### ashclouded

I substituted t into d(t) = -5e^(-5t) cos (10t) and then on the graph I changed the value d(t) = -5e^(-2t) cos (10t) which in turn when graphed changed the time when the damper had converged to about 0 at pi/3 and lengthened the time

4. Jun 5, 2014

5. Jun 5, 2014

### ashclouded

The rod is stable when the Y-Axis (Deflection) is equal to zero and so I lengthened the time (X-axis) it took for it to have the deflection = 0
Does that make sense?

6. Jun 5, 2014

### LCKurtz

Not to me. With that model it continues vibrating around $y=0$ so it would never be "stable". You can't assume we have attended your class and read your book. We aren't mind readers here. You have to give us enough information so that we understand the problem. So far, I have no clue what you are really trying to do.

7. Jun 6, 2014

### haruspex

I have no idea what that's asking for.
How can a mathematical model lengthen a time?
What does it mean to lengthen a time by a given time... make it longer by a specified amount? A specified ratio seems more likely.

8. Jun 6, 2014

### Ray Vickson

The only way the question makes sense (physically or engineering-wise) would be if you could vary the design, so that you could change the '0.5', '5' and/or '10' to some other values to get behavior closer to what you want.