Barton's Pendulum
Oscilations
Pendula
A pendulum consists of an arm of low mass with a bob, which has a higher mass, on the end. The top of the arm is pivoted so that the pendulum can swing. A pendulum will continue to swing back and forth indefinately, until it is stopped by air friction and friction within the pivot. When the angle, á, between the stationary line of the pendulum (the line towards which the movement tends) and the line of maximum amplitude of the pendulum is quite small, then the time period of the pendulum can be found according to the following equation: , where l is the length of the arm of the pendulum (between the pivot and the centre of mass of the bob) and g is the acceleration due to gravity (on earth ñln9.81). For the spring, a similar equation can be derived. For any spring, , where m is the mass of the bob on the spring and k is hookes constant. Hookes constant is the constant of proportionality of force against extension for any spring, and varies from spring to spring. In formulaic terms. . The unit for thisd quantity is newtons per metre. Substituting the above equation (Hooke's Law) into the equation, , and therefore, . g here is the acceleration due to gravity, as the force on the spring consists of the weight of the bob. On the moon, the time period of the pendulum would change, as l is a constant where as g would change, where as the time period of the spring would stay constant, as is a constant, and x changes proportionally to g.
What connects the motion of both the spring and the pendulum? They are connected by the fact that they both move with simple harmonic motion (SHM), which is the most common form of motion, as it is related to circular motion, and also to the motion of pendula, springs, logs in th water, water in a u-tube, pulsars, vibrating molecules, etc.
What is simple harmonic motion? it is motion in which:
1. The motion (and the acceleration) is directed towards a fixed point.
2. The acceleration is proportional to
Pendula
A pendulum consists of an arm of low mass with a bob, which has a higher mass, on the end. The top of the arm is pivoted so that the pendulum can swing. A pendulum will continue to swing back and forth indefinately, until it is stopped by air friction and friction within the pivot. When the angle, á, between the stationary line of the pendulum (the line towards which the movement tends) and the line of maximum amplitude of the pendulum is quite small, then the time period of the pendulum can be found according to the following equation: , where l is the length of the arm of the pendulum (between the pivot and the centre of mass of the bob) and g is the acceleration due to gravity (on earth ñln9.81). For the spring, a similar equation can be derived. For any spring, , where m is the mass of the bob on the spring and k is hookes constant. Hookes constant is the constant of proportionality of force against extension for any spring, and varies from spring to spring. In formulaic terms. . The unit for thisd quantity is newtons per metre. Substituting the above equation (Hooke's Law) into the equation, , and therefore, . g here is the acceleration due to gravity, as the force on the spring consists of the weight of the bob. On the moon, the time period of the pendulum would change, as l is a constant where as g would change, where as the time period of the spring would stay constant, as is a constant, and x changes proportionally to g.
What connects the motion of both the spring and the pendulum? They are connected by the fact that they both move with simple harmonic motion (SHM), which is the most common form of motion, as it is related to circular motion, and also to the motion of pendula, springs, logs in th water, water in a u-tube, pulsars, vibrating molecules, etc.
What is simple harmonic motion? it is motion in which:
1. The motion (and the acceleration) is directed towards a fixed point.
2. The acceleration is proportional to