Question

3. A gun barrel of mass $m = 500$ kg has a recoil spring of stiffness $k = 3,00,000$ N/m. As the gun shoots, it recoils with a velocity $v = 29.4$ m/s and compresses the spring up to some distance $x$. When the gun reaches the extreme position, a dashpot (a damping machine whose working mechanism we are not concerned with) gets activated so that the gun slowly returns to its original place of firing. For your convenience, the configurations has been described in the figure below. Given the information, find the following: (a) The value of $x$. (b) Critical damping coefficient of the dashpot. (c) Time required for the barrel to return to a position 50mm from the initial position.

          3. A gun barrel of mass $m = 500$ kg has a recoil spring of stiffness $k = 3,00,000$ N/m. As the gun shoots, it recoils with a velocity $v = 29.4$ m/s and compresses the spring up to some distance $x$. When the gun reaches the extreme position, a dashpot (a damping machine whose working mechanism we are not concerned with) gets activated so that the gun slowly returns to its original place of firing. For your convenience, the configurations has been described in the figure below.

Given the information, find the following:
(a) The value of $x$.
(b) Critical damping coefficient of the dashpot.
(c) Time required for the barrel to return to a position 50mm from the initial position.

3. A gun barrel of mass m = 500 kg has a recoil spring of stiffness k = 3,00,000 N/m. As the gun shoots, it recoils with a velocity v = 29.4 m/s and compresses the spring up to some distance x. When the gun reaches the extreme position, a dashpot (a damping machine whose working mechanism we are not concerned with) gets activated so that the gun slowly returns to its original place of firing. For your convenience, the configurations has been described in the figure below.

Given the information, find the following:
(a) The value of x.
(b) Critical damping coefficient of the dashpot.
(c) Time required for the barrel to return to a position 50mm from the initial position.

Added by Juan Francisco B.

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