I have a problem and I want to determine the friction coefficient using diffential equations i.e. solving the equation (this is from a Under-damped Oscillator)
$$ m\ddot x+c\dot x+kx=0. $$
Suppose I know the mass of the object, the initial distance from the origin, the constant of the spring, and the time in which the object is stopped. Can I solve my problem with this data? Also is there a better way to determine the friction coefficient using differential equations?