A railway buffer consists of a pair of cylinders placed parallel side-by-side. Oil is present in each cylinder and is arranged to bypass through ports, thereby producing a damping resistance, which is proportional to the velocity of the piston within the cylinder. The magnitude of this resistance is 50 kN at a velocity of 0.25 m/s. Each cylinder also contains a compression spring, initially with negligible compression, of stiffness 65 kN/m. A rigid train of mass 260 tons is moving at a speed of 2 m/s and collides with the buffer. Determine the time and distance taken by the train before first coming to rest. Assuming that the train comes into contact and then becomes attached to the free end of the buffer.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
A railway buffer consists of a pair of cylinders placed parallel side-by-side. Oil is present in each cylinder and is arranged to bypass through ports, thereby producing a damping resistance, which is proportional to the velocity of the piston within the cylinder. The magnitude of this resistance is 50 kN at a velocity of 0.25 m/s. Each cylinder also contains a compression spring, initially with negligible compression, of stiffness 65 kN/m. A rigid train of mass 260 tons is moving at a speed of 2 m/s and collides with the buffer. Determine the time and distance taken by the train before first coming to rest.
Assuming that the train comes into contact and then becomes attached to the free end of the buffer.
Note: You are also expected to provide a plot(s) to show the position and velocity of the train. The plot(s) can be produced using Matlab, Excel,
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can i have the steps and commands used to plot the graph in matlab
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