- #1
atqamar
- 55
- 0
I'm having a hard time evaluating this integral.
A Gaussian pulse \psi (y,t) = Ae^{-( \frac{y-ct}{a} )^2} is traveling in an infinite string of linear mass density \rho, under tension T.
I know the Kinetic Energy is the integral of the partial: \frac{\rho}{2} \int_{-\infty}^{\infty} (\frac{\partial \psi}{\partial t})^2 dy. I evaluate the partial, and this simplifies to \frac{\rho}{2} \int_{-\infty}^{\infty} (\frac{2c(y-ct)}{a^2} \psi)^2 dy.
I don't know where to proceed from here. I tried u-substitution, and integration by parts, with no success. I think the error function is useful in this, but we haven't covered this in the physics course yet.
A Gaussian pulse \psi (y,t) = Ae^{-( \frac{y-ct}{a} )^2} is traveling in an infinite string of linear mass density \rho, under tension T.
I know the Kinetic Energy is the integral of the partial: \frac{\rho}{2} \int_{-\infty}^{\infty} (\frac{\partial \psi}{\partial t})^2 dy. I evaluate the partial, and this simplifies to \frac{\rho}{2} \int_{-\infty}^{\infty} (\frac{2c(y-ct)}{a^2} \psi)^2 dy.
I don't know where to proceed from here. I tried u-substitution, and integration by parts, with no success. I think the error function is useful in this, but we haven't covered this in the physics course yet.
