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# Inside Pt.2 - Peak Of The Pendulum - Demo 3 (CDr)

9

2010
Label: Not On Label (Peak Of The Pendulum Self-Released) - none • Format: CDr • Country: Canada • Genre: Rock •

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A simple pendulum is defined to have an object that has a small mass, also known as the pendulum bob, which is suspended from a light wire or string, such as shown in Figure 1. Exploring the simple pendulum a bit further, we can discover the conditions under which it performs simple harmonic motion, and we can derive an interesting expression.

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T is the period of oscillations - time that it takes for the pendulum to complete one full back-and-forth movement. L is the length of the pendulum (of the string from which the mass is suspended). g is the acceleration of gravity. On Earth, this value is equal to m/s^2 - this is the default value in the simple pendulum calculator.

c d θ a t ; (3) where a t a axis is the acceleration of the ground respon-sible for the pendulum’s motion. Combining equations (1) to (3) with M1 M2 g R one obtains I cm M d c d 2 θ d d Mgθ≈ d d Ma t: (4) Becauseoftheparallel-axistheorem(Becker,),theterm in brackets multiplying the angular acceleration is .

The double pendulum is a very interesting system as it is very simple but can show chaotic behavior for certain initial conditions. In this regime, slightly changing the initial values of the angles ($\theta_1,\theta_2$) and angular velocities ($\dot{\theta}_1,\dot{\theta}_2$) makes the trajectories of the bobs become very different from the.

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Physical pendulum (review !) θ So rod has smaller T than simple pendulum of same L Notice: m doesn’t matter! 2 2 l l m I g T = π g L mL mL g L T 2π 2π 2 2 = = For a simple pendulum, bob = a point mass (I = m l2), and l = L, so If the pendulum is a solid rod, (I = m L2 / 3), and CM is located at its center (l = L / 2) g L L m mL g L.