Question

The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system. r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by dt m dt m where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and r(t) is the downward displacement of the mass. 2. Find the homogenous solution, Th , to the ODE above, given m = 1 , c-40 and k 144. 3. Solve the particular solution, Tp, given r(t)24t(t - 1) 4. Apply initial conditions (0 0 and '(0)0 to get a specific solution to the ODE. 5. Based on your solution from Q4, solve the net force (ie. 2F) that acts on the mass. Plot the external force and the net force from t = 0 to t1 and comment on the effect the suspension system is having on force experienced by the rider

Answer 1

the SP? dt1 dt (or) C, T(t) 2Fin he h

+ 201, 256 536t 36t 36t Solve e palili So

goA +144 B- 24 3 3 2 432 36 t 6 2 132 32- -36t で一 2 지이_ -4G-364 t-

Ч 32. 27 432 29 34 SL -34 3454 4t2 오才 34 S6 3456 -36H χ(k) 2 <32 34 S