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Essay / Reflection of the physics of a pendulum - 1413
A pendulum is described as a point mass suspended by a string of negligible mass. Typically, it rests in its equilibrium position, but once moved, the point mass will begin to oscillate back and forth around its fixed position. The movement repeats regularly and the period can be predicted. The model T=2π√(L/g) predicts the period of the pendulum, where L is the length of the string. According to this formula, the magnitude of the displacement plays no role in the duration of an oscillation. But how is this possible? Experiments have shown that for any angle of the pendulum less than or equal to 90 degrees from the rest position, it actually holds. Of course, the pendulum will eventually stop due to external forces, such as wind resistance and restoring force. The restoring force is the force that tends to bring a system back to equilibrium. It is this force that causes the pendulum's movement to slow down as it travels away from the point of rest, and then speed up again on its return journey. Momentum is the force that carries the bobsled past the balance point, where the restoring force slows it down again to begin repeating the cycle. But what forces actually act on the bob itself? There are only two, the force of gravity and the tension force of the string, which acts upwards towards the pendulum's pivot point. Of course, gravity is easy to predict. This is a downward force of 9.81 m/s2. The tension force is not always constant, because its magnitude and direction are constantly changing as the pendulum swings. The direction is always towards the pivot point. When at rest, the tension is straight up, but if the movement is right, the direction is up and left, etc. This image shows the forces acting on a pendulum moving at 5 different points throughout half a year. doesn't it simply remain stuck between the two opposing forces at its equilibrium point? To answer this question, we need to break down one of the forces into its component parts. Since the tension force is always perpendicular to the path of motion, we will break gravity. It consists of a component that is in the direction of the bob's acceleration (Fgrav-tangent) and another that is directly opposite that of the tension force (Fgrav-perp), as shown in the diagram of the free body below. The gravity vector is always the sum of these two vectors. Image[5 steps] When the pendulum swings, the two component vectors change direction. Fgrav-tangent is always tangent to the arc which is the movement of the pendulum, and Fgrav-perp is always perpendicular to it. Fgrav-tangent acts as a restoring force. As the bob moves to one side of the equilibrium point, the tangent Fgrav points in the opposite direction, slowing the bob until it reverses direction toward equilibrium. Picture[5