The Reflection Of The Physics Of A Pendulum

A pendulum is described as a point mass suspended by a string of negligible mass. Typically, it rests in its equilibrium position, but once displaced, the point mass will begin to swing back and forth, about its fixed position. The motion repeats regularly, and the period can be predicted. The model T=2π√(L/g) predicts the period if the pendulum, where L is the length of the string. According to this formula, the amount of displacement plays no role in the length of time an oscillation takes. But how is that possible? Experiments have shown that with any angle of the pendulum less than or equal to 90 degrees from rest position, it in fact holds up. Of course, the pendulum will stop eventually due to outside forces, such as wind resistance and

The restoring force is the force that tends to bring a system back towards equilibrium. It is this force that causes the pendulum bob to slow down on its way away from the resting point, and speed up again on its return trip. Momentum is the force that carries the bob past the equilibrium point, where the restoring force slows it yet again to begin the repeating of the cycle. But what forces are actually acting on the bob itself? There are only two, the force of gravity and the tension force from the string, which acts upwards towards the pivot point of the pendulum. Gravity, of course, is easy to predict. It is a downwards force of 9.81 m/s2 . The tension force is not always constant, as both its magnitude and its direction are constantly changing as the pendulum swings. The direction is always towards the pivot point. When it is at rest, the tension is straight up, but if the bob is to the right, the direction is up and to the left, etc. This image shows the forces acting on a pendulum in motion at 5 different points throughout half an

Why doesn’t it just get stuck in between the two opposing forces at its equilibrium point? To answer that, we need to break one of the forces down into its components. Since the tension force is always perpendicular to the path of motion, we will break down gravity. It consists of one component that is in the direction of the acceleration of the bob (Fgrav-tangent), and another that is directly opposite that of the tension force (Fgrav-perp), as seen in the free- body diagram below. The gravity vector is always the sum of these two vectors.

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As the pendulum swings, both of the component vectors change direction. Fgrav-tangent is always tangent to the arc that is the motion of the pendulum, and Fgrav-perp is always perpendicular to it. Fgrav-tangent acts as the restoring force. As the bob moves to one side of the equilibrium point, Fgrav-tangent points in the opposite direction, slowing the bob until it reverses its direction back to the equilibrium.

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