How to solve kinematic system with spring and pulleys?

[okan.00]

Hello everyone,
i tried to solve this excercise of the kinematic and im not sure if my calculations are correct. Please give me feedback and help for c).

The text is in german, it says:
A massless and inextensible rope attached to the ceiling is guided around a massless pulley 3 and then around a homogeneous cylindrical pulley 1 (mass m, radius r) and carries a point mass 2 (m2) at the end. The pulley 3 is attached to the environment at its center point by a spring (stiffness c). in the position shown, the spring is pretensioned to tension with the force Fv. The system is released from rest. As a result of the acceleration due to gravity, mass 2 moves downwards (coordinate x) and pulley 1 rotates clockwise. The frictional torque Mr acting in the bearing of roller 1 is therefore counterclockwise

a) By what amount is the spring in the drawn position already elongated compared to its relaxed length?
b) Determine the velocity of the mass m2 as a function of the coordinate x
c) What is the maximum deflection of the mass m2

 

[okan.00]

Excercise

 

[okan.00]

a)

 

[rb1957]

A force, Fv, is applied to the spring (to pretension it)

1) is a force of Fv/2 being applied to m2 ? or

2) is Fv being applied directly to the spring ? and

3) does it matter ?? (I think it does)

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[okan.00]

Sorry, i dont understand how your response is gonna help me?

 

[prex]

The answer to a) should simply be F[sub]V[/sub]/c=r/2
The answer to c) should come from b) by calculating x from v(x)=0
Your solution to b) is not far from being correct. The energy stored in the spring is c x[sup]2[/sup]/8, as the spring elongates by x/2.
By replacing J[sub]1[/sub] and ω[sub]1[/sub] with their expressions you'll be almost done.

prex
[URL unfurl="true"]http://www.xcalcs.com[/url] : Online engineering calculations
[URL unfurl="true"]https://www.megamag.it[/url] : Magnetic brakes and launchers for fun rides
[URL unfurl="true"]https://www.levitans.com[/url] : Air bearing pads