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The length of a simple pendulum is $0.63 \mathrm{m},$ the pendulum bob has a mass of 295 $\mathrm{g}$ , and it is released at an angle of $15^{\circ}$ to the vertical. (a) With what frequency does it oscillate? (b) What is the pendulum bob's speed when it passes through the lowest point of the swing? Assume SHM. (c) What is the total energy stored in this oscillation assuming no losses?

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a. $$0.63 \mathrm{Hz}$$b. $$0.65 \mathrm{m} / \mathrm{s}$$c. $$0.062 \mathrm{J}$$

Physics 101 Mechanics

Chapter 14

Oscillators

Motion Along a Straight Line

Motion in 2d or 3d

Periodic Motion

Cornell University

Hope College

McMaster University

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

02:18

In physics, an oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The oscillation may be periodic or aperiodic.

03:58

The length of a simple pen…

05:07

(II) The length of a simpl…

05:27

05:12

A simple pendulum has a le…

06:17

A simple pendulum is swing…

10:13

(III) Consider a simple pe…

02:59

so here for party When you want to find the frequency, the frequency is simply gonna be won over to pi times the square root of G divided by all. And so the frequency is gonna be one over to pie times the square root of 9.8 divided by 0.63 meters and we find that the frequency is equaling 0.6 to 8 hertz. Now, this would be your answer for party part B now wants us to find the maximum velocity. So for party, we can stay that the energy of the top would be equal to the energy at the bottom. Eso weaken. We can say that mg l minus l co sign of theta This essentially be the gravitational potential energy. This will all be converted into kinetic energy. So envy Max squared. So, essentially, at this point, we can say that he is going to be equal to two times g times l one minus co sign of stada and this will be to the 1/2 power at Ah. Now we can say that the is going to be equal 22 times 9.8 times 0.63 meters times one minus CO sign of 15 degrees, all to the 1/2 power and we find that the velocity is gonna be equal to a 0.649 meters per second. Again, this is ah, bee at the bottom. And lastly, we have to find the total amount of energy. The total amount of energy can simply be equal to 1/2 and the Max square. And so this is simply going to be able to 1/2 times the mass of point 295 kilograms, and then this will be multiplied by 0.649 squared, and we find that the total money and energy associated with this system is gonna be equal toe 0.6 to 1. Jules. So this would be our final answer for part C. That is the end of the solution. Thank you for watching

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