Shape of string pulled upward by point force at one end

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Twukwuw
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Can anyone solve this... "shape of a string" puzzle?

Let's say there is an infinite massless and elastic string, which laid horizontally and one of the ends is extended to infinite distance.
The string is "pulled" thoroughly and somehow, so that there is a tension T along it.
There is a CONSTANT force F acting upwards on the other end(at the POINT) :eek: , which will then "drag" the nearer part of the string upwards.
My question is simple,
What will be the wave profile(or the shape of the wave) after a duration t?

Is it a curve...or is it a combination of 1 section of slope string and 1 section of horizontal string? The horizontal section of the string "haven't experience the force yet."

Assume there is no other force other than F. The force F ONLY acts at the "end-POINT" of the string.

Welcome anyone who like to accept challenge.
Thanks.

Twukwuw. :biggrin:
 

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What will be the acceleration of the end where upward force is applied? (The string is massless)
 
The dynamics of an elastic string, finite or infinte, are discussed in many textbooks -- classical mechanics(Goldstein, Synge&Griff), quantum field theory(Zee, Gross), E&M(Jackson, Panofsky and Phillips), mathematical physics (Courant&hHilbert). As the end is lifted, it will generate waves in the string -- unless the lifting is adiabatic. Your problem is relatively standard -- a good problem for an advanced mechanics final exam.

Regards,
Reilly Atkinson
 
sorry, correction here:
the string has mass,
its mass is uniformly distributed along the line.
thanks~!
 
good, if it didnt had a mass it would have to move at the speed of light