Solving a Second Order Differential Equation

Find the general solution of this differential equation: $$\frac{d^{2}\psi}{dt^{2}}+A\psi=0$$

This SWBQ is a quick check to see if students realize that the solution to this differential equation depends on the sign of $A$. Try this SWBQ whenever this equation comes up in physics (often!), using whatever algebraic symbols are relevant for the problem at hand. EVENTUALLY students start to recognize the equation in its many guises.

Resist the temptation to signal the sign of $A$ by giving the prompt in the standard physics form: $$\frac{d^{2}\psi}{dt^{2}}+\omega_{o}^{2}\psi=0$$

Powerpoint slide
PDF slide