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## Summary:

- Finding motion by making a differential equation using initial values and an acceleration that depends on position and time.

## Main Question or Discussion Point

I have computed that the acceleration in my problem is

a(t) = -gj - k/m(|r(t)| - L_0) * r(t)/|r(t)|

Where a(t) is the acceleration vector, g is the gravitational acceleration, j is the unit vector in y-direction, k is the spring constant, m is the mass, r(t) is the position vector, |r(t)| is the length of r(t) and L_0 is the equilibrium length of a rope. I am asked in my problem to make a differential equation by using some initial values and the acceleration to compute the motion.

I was told by the teacher not to use the equations of motion because those require a constant acceleration, while the one we have here is dependent on the position. Is there a way for me to compute the motion given an initial velocity and position?

a(t) = -gj - k/m(|r(t)| - L_0) * r(t)/|r(t)|

Where a(t) is the acceleration vector, g is the gravitational acceleration, j is the unit vector in y-direction, k is the spring constant, m is the mass, r(t) is the position vector, |r(t)| is the length of r(t) and L_0 is the equilibrium length of a rope. I am asked in my problem to make a differential equation by using some initial values and the acceleration to compute the motion.

I was told by the teacher not to use the equations of motion because those require a constant acceleration, while the one we have here is dependent on the position. Is there a way for me to compute the motion given an initial velocity and position?

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