Question

For a cart oscillating on a spring, let’s say the initial position, initial velocity, and initial acceleration are known. Could someone use the formula x=x0+v0t+1/2at^2 to find the cart’s position at a later time? Why or why not?

Answer 1

Yup you can always revert back to using the good old Kinematic Equations we all learn in intro physics, but the rule of thumb is, don't make it harder than it needs to be. If you can use a simpler concept, use it! I suggest conservation of energy here but.... anyway to answer your question: yes.

Here's how:

since you already know the initial velocity and initial position, the only thing you don't know is a. But we can use F = ma to find a. Namely:
a = F/m

But this is for a spring system so the force that the spring exerts on the box is F = -kx.

There you go, you have everything.

Therefore: a = F/m = (-kx)/m
So

x = x0 + v0*t + .5 * [(-kx)/m] * t^2 all you have to is solve for x and you will have x as a function of t. Easy :)

Answer 2

no this equation can not be used because this equation is only valid in the cases of constant acceleration.......here spring exerts a variable force depending on the elongation/compression in spring.....so u cant use this equation