ratio. 4 A pneumatic spring consists of a piston riding on top of the air in a cylinder. The upward force of the ai...
ratio. 4 A pneumatic spring consists of a piston riding on top of the air in a cylinder. The upward force of the air on the piston is given by Fair 14, where a is a constant with funny units of N m14 For simplicity, assume the air only supports the weight, Fw, of the piston itself, although in practice this device is used to support some other object. The equilibrium position, ro, is where Fw equals -Fair (Note that in the main text I have assumed the equilibrium position to be at r - 0, but that is not the natural choice here.) Assume friction is negligible, and consider a case where the amplitude of the vibrations is very small. Let a 1.0 N m14, Zo = ¡.00 m, and Fw =-1.00 N. The piston is released from r = 1.01 m. Draw a neat, accurate graph of the total force, F, as a function of x, on graph paper, covering the range from a 0.98 m to 1.02 m. Over this small range, you will find that the force is very nearly proportional to a-o. Approximate the curve with a straight line, find its slope, and derive the approximate period of x ai Problem 4 oscillation
ratio. 4 A pneumatic spring consists of a piston riding on top of the air in a cylinder. The upward force of the air on the piston is given by Fair 14, where a is a constant with funny units of N m14 For simplicity, assume the air only supports the weight, Fw, of the piston itself, although in practice this device is used to support some other object. The equilibrium position, ro, is where Fw equals -Fair (Note that in the main text I have assumed the equilibrium position to be at r - 0, but that is not the natural choice here.) Assume friction is negligible, and consider a case where the amplitude of the vibrations is very small. Let a 1.0 N m14, Zo = ¡.00 m, and Fw =-1.00 N. The piston is released from r = 1.01 m. Draw a neat, accurate graph of the total force, F, as a function of x, on graph paper, covering the range from a 0.98 m to 1.02 m. Over this small range, you will find that the force is very nearly proportional to a-o. Approximate the curve with a straight line, find its slope, and derive the approximate period of x ai Problem 4 oscillation