On a nice weekend day, as you are riding your bicycle around in West Lafayette you make a wrong turn and end up riding on the infamously rough Lindberg Road by the Celery Bog. (The Lindberg Road was fixed around a decade ago - so imagine this ride look place before then). Assume that the road surface profile varies harmonically with t 6 cm undulations about a mean elevation. The distance between consecutive peaks of these undulations is 2 m. Assume that all the "suspension" in your bike is thanks to springs under the seat of your bike. When you sit on the seat of your bike for your casual ride, the springs compress 5 cm under your weight. When you are seated, the damper under the seat provides an equivalent linear viscous damping of 10% of the critical damping. A simple representation of your ride on the "never-ending" rough road is shown below. a. If you are riding your bicycle at a horizontal speed v of 2.5 m/s, how much bumping up and down will you experience? In other words, what is the maximum vertical displacement you will experience? b. On another Lindberg Road bike ride, you are carrying a backpack full of books for your classes. The backpack increases your on-seat weight by 20%. Assuming that you are still able to ride at v=2.5 m/s, will this "loaded" ride be more or less comfortable than your previous, "no backpack" ride? EMB K2 K2 16cm