ENGG2013 Unit 22Modeling byDifferential EquationsApr, 2011
ENGG2013 Unit 22 Modeling by Differential Equations Apr, 2011
FREE FALLING BODYkshum2
FREE FALLING BODY kshum 2
Height, velocity and accelerationParabola2010y = -5t2+150-1010.51.502t> -10v=-10t-2050.5011.52t-9a =-1010-1100.511.52t3kshum
Height, velocity and acceleration • Parabola kshum 3 0 0.5 1 1.5 2 -10 0 10 20 t y 0 0.5 1 1.5 2 -20 -10 0 t v 0 0.5 1 1.5 2 -11 -10 -9 t a y = –5t2+15 v = –10t a = –10
Newton's law of motionAssumenoairfriction. F=ma-Force = mass x acceleration-a = y"(t) F=mg Gravitational Force is proportional to the mass,the proportionality constant g ~ -1o ms-2y"(t) = gkshum
Newton’s law of motion • F = ma – Force = mass acceleration – a = y’’(t) • F = mg – Gravitational Force is proportional to the mass, the proportionality constant g –10 ms-2 . kshum 4 y’’(t) = g Assume no air friction
Differential eguation· A differential equation is an equationwhich involves derivatives.Examples:dx/dt = x + 2tThe variable x is a function of time td2y/dt2 = t2 + y2The variable y is a function of t.kshum5
Differential equation kshum 5 • A differential equation is an equation which involves derivatives. • Examples: The variable x is a function of time t. The variable y is a function of t. dx/dt = x + 2t d 2y/dt2 = t2 + y2