I am having trouble with a combined function task. It is a mass that is attached to a spring, and a spring to a wall (think, a doorstop). When it is pulled away from the wall it oscillates along the floor, however due to friction on the floor it slows down as it approaches 0. Along the lines of a dampened sine wave. The function we need is: d(t) = f (t)× g(t) + r It follows the following parameters: • The mass is at a resting position of r = 30 cm. • The spring provides a period of 2 s for the oscillations. • The mass is pulled to d = 50 cm and released. • After 10 s, the spring is at d = 33 cm.
I can't figure out how to write an equation of this model if anyone could help that would be great.
Let us measure the position $x$ from the equilibrium position. Is the $2$ second period when there is friction? I will assume so. The solution is $x=A \exp (- b t) \cos (\omega t)$. The given data gives $A=20$ and $\omega=\frac \pi 2$and we can then calculate $b$.