A motocross motorcycle weighs 100kg, and we assume a rider weight of 80kg. When the rider mounts the motorcycle, the suspension compresses 10 cm, then comes to rest at equilibrium. The suspension system provides damping equal to 240 times the instantaneous vertical velocity of the motorcycle (and rider). 1. Set up the differential equation that models the behavior of the motorcycle suspension system.
2. We are interested in what happens when the motorcycle lands after taking a jump. Let t=0 when the motorcycle first contacts the ground. If the motorcycle hits the ground with a velocity of 3m/s downward, find the equation of motion of the motorcycle after the jump.
3. Graph the equation of motion over the first second after the motorcycle hits the ground