Recent content by baranij

Hello, Would it also hold true if the limits of integration are other than 0 to infinity that \int_{ }^{ } \cos (x^{2}) dx = \int_{ }^{} \sin (x^{2}) dx ? What about if x^{a} (x is raised to an arbitrary power like? \int_{ }^{ } \cos (x^{3}) dx Thank you for the help.

Thank you, that's some very good points. I am trying to keep this as simple as possible and don't want to model a gas damper, just a regular coil spring with a constant damping coefficient damper. What I'm trying to figure out is the reaction to a specific initial condition...lets say a 2...

I managed to combine equations 2 and 4 to get the following. K_{W}a \ + \ C_{W}\dot{a} \ + \ R^{2}K_{X}e \ + \ R^{2}C_{X}\dot{e} \ = \ \left(K_{W} + R^{2}K_{X}\right)b \ \ + \ \left(C_{W} + R^{2}C_{X}\right)\dot{b} \ -\ M_{W}\ddot{b} To keep things simple...

Spring Mass Damper Solution of a Motorcycle Suspension I am trying to create a model of a motorcycle suspension to figure how road bump forces get transferred to the bike. I have created a free body diagram of the system and also attached a pdf. If you need the original powerpoint in case...

To solve for time based on initial and final speed: \int_{t_{0}}^{t_{F}} dt = \int_{v_{0}}^{v_{F}} \frac{dv}{\frac{A}{v} - Bv^{2}} \int dt = \int (\frac{{v}}{A-Bv^{3}}) dv Now that the v on top of the fraction is not a derivative of the bottom A-Bv^{3}, can you suggest a...

OK, Here goes again: \int_{x(0)}^{x} dx = \int_{v(0)}^{v} \frac{vdv}{\frac{A}{v} - Bv^{2}} \int dx = \int (\frac{{v^{2}}}{A-Bv^{3}}) dv \int dx = \int (\frac{1}{A-Bv^{3}}) v^{2} dv = \frac{1}{-3B}\int (\frac{1}{A-Bv^{3}}) (-3B)v^{2} dv u=g(x)=(A-Bv^{3}) ...&...

\int_{x(0)}^{x} dx = \int_{v(0)}^{v} \frac{vdv}{\frac{A}{v} - Bv^{2}} The integral on the left is a simple substitution and the integral on the right is elemental. \int dx = \int (\frac{{v^{2}}}{A-Bv^{3}}) dv \int dx = \int (\frac{1}{A-Bv^{3}}) v^{2} dv...

Its been 7 years since college so I'm a bit rusty in my Integration, but don't you get: \int \frac{dv}{g(v)} = \int {d(x)}{h(x)} from: \frac{dv}{dx} = g(v) h(x) instead of: \int \frac{dv}{g(v)} = \int \frac{dx}{h(x)} Now I'm a bit confused as to what h(x)...

Your 1st one is the problem at hand: a(v) = \frac{A}{v} - Bv^{2} I've used the chain rule and tried to integrate but get stuck on trying to separate out Vfinal in terms of Vinitial and \DeltaX. So far I've always had Vfinal in terms of \DeltaX AND time. The integration is killing...

Thank you for the reply. a(v) = A/v-B*v^2 where a=acceleration, v=velocity The acceleration is not constant it varies depending on the velocity. Where I am getting stuck is the integrating. The "A/v" term when integrated ends up being a "ln(v)" and I can't separate "v" out of the...

1st I am having problems getting a solution for final Velocity in terms of Distance traveled with a non-zero initial velocity. Acceleration = A / Velocity - B * Velocity^2 where A is a constant related to Hp (horsepower) of the vehicle and and B is a constant related to aerodynamic...