# What speed v(t) enables constant power by solenoid pull?

cairoliu
Assuming the position x = 0 if no air gap, max stroke of plunger is L.
Bordery conditions: x(t=0) = L, x(t=T)= 0.
Given magnetic force F(x) = kx(t)^-2, here k is constant.
If uncontrolled, there is big crash noise afer solenoid actuated, so I wish it pull plunger at constant power.
Help me find the dynamic position x(t), then I can get velocity.
I know Wolfram software may resolve it, but I have no money to buy it.

Gold Member
Bordery conditions: x(t=0) = L, x(t=T)= 0.
Given magnetic force F(x) = kx(t)^-2, here k is constant.
If uncontrolled, there is big crash noise afer solenoid actuated, so I wish it pull plunger at constant power.
If x(t=T)= 0, then F(x(t=T)) = kx(t=T)^-2 = k(0)^-2 = ##\infty##. How do you expect not having a big crash noise at t=T ?

cairoliu
If x(t=T)= 0, then F(x(t=T)) = kx(t=T)^-2 = k(0)^-2 = ##\infty##. How do you expect not having a big crash noise at t=T ?
Now that noise not good, I can reserve a minimal air gap 𝛿, then x(t=T)= 𝛿, and still ask for the solution of constant power.

• 