- #1
yosimba2000
- 206
- 9
This is not a HW/coursework problem. Just something I randomly thought about.
1. Homework Statement
There is a horizontal spring with a mass at the end of it. The mass has an initial velocity V that compresses the spring. Find the equation of motion for this mass without using energy equations.
At any displacement X, force by spring is F = -kx
Force on mass by spring = -m* (applied acceleration on mass by spring) = -ma
Equation of motions:
Vf^2 - Vi^2 = 2ax
As the displacement changes, then the force and hence acceleration provided by the spring against the mass is also changing. So acceleration against mass is function of distance.
F = -kx = -ma
a = kx/m
Vf^2 - Vi^2 = 2ax <-- plug in a
Vf^2 - Vi^2 = 2 (kx/m)x
Vf^2 = 2 (kx/m)x + Vi^2
Did I do it right?
1. Homework Statement
There is a horizontal spring with a mass at the end of it. The mass has an initial velocity V that compresses the spring. Find the equation of motion for this mass without using energy equations.
Homework Equations
At any displacement X, force by spring is F = -kx
Force on mass by spring = -m* (applied acceleration on mass by spring) = -ma
Equation of motions:
Vf^2 - Vi^2 = 2ax
The Attempt at a Solution
As the displacement changes, then the force and hence acceleration provided by the spring against the mass is also changing. So acceleration against mass is function of distance.
F = -kx = -ma
a = kx/m
Vf^2 - Vi^2 = 2ax <-- plug in a
Vf^2 - Vi^2 = 2 (kx/m)x
Vf^2 = 2 (kx/m)x + Vi^2
Did I do it right?