- #1
shyta
- 56
- 0
Homework Statement
A point mass m moving along the z axis experiences a time dependent force and a fricitional force. Solve the equation of motion
m[itex]\ddot{z}[/itex] = -m[itex]\gamma[/itex][itex]\dot{z}[/itex] + F(t)
to find v(t) = [itex]\dot{z}[/itex](t) for the initial velocity [itex]\dot{z}[/itex](0) = v_0
Hint: what is the time derivative of [itex]e^{\gamma t}[/itex]v(t)
The Attempt at a Solution
So I made use of the hint and got [itex]e^{\gamma t}[/itex] ([itex]\ddot{z}[/itex](t) + [itex]\gamma[/itex][itex]\dot{z}[/itex](t) )
Manipulating the equation of motion, I got [itex]e^{\gamma t}[/itex] ([itex]\ddot{z}[/itex](t) + [itex]\gamma[/itex][itex]\dot{z}[/itex](t) ) = [itex]e^{\gamma t}[/itex] 1/m F(t)
Subbing in the hint and integrating: [itex]\dot{z}[/itex](t) = [itex]e^{-\gamma t}[/itex]/m [itex]\int[/itex] [itex]e^{\gamma t}[/itex] F(t) dt
Just wondering if this is correct? and how do I make use of the initial condition v_0?