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(II) A simple pendulum is 0.30 $\mathrm{m}$ long. At $t=0$ it is released from rest starting at an angle of $13^{\circ} .$ Ignoring friction, what will be angular position of the pendulum at (a) $t=0.35 \mathrm{s},$ (b) $t=3.45 \mathrm{s},$ and $(c) t=6.00 \mathrm{s?}$

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a. $$-5.41^{\circ}$$b. $$8.41^{\circ}$$c. $$-12.53^{\circ}$$

04:59

Shital Rijal

03:28

Keshav Singh

Physics 101 Mechanics

Chapter 14

Oscillators

Motion Along a Straight Line

Motion in 2d or 3d

Periodic Motion

Cornell University

Rutgers, The State University of New Jersey

University of Winnipeg

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.

0:00

(II) A simple pendulum is …

02:58

A simple pendulum is $0.30…

01:01

A simple pendulum is 0.32 …

04:22

(III) A clock pendulum osc…

01:59

04:27

A simple pendulum is 0.48 …

03:07

A clock pendulum oscillate…

04:31

If all frictional effects …

02:32

The angular displacement o…

02:13

The angular position of a …

01:37

03:00

A simple pendulum with len…

01:22

Let the position of a swin…

01:09

A simple pendulum having l…

03:32

The pendulum consists of a…

01:19

The pendulum oscillates ab…

now her in this question we are given that a simple pendulum that has a length of 0.3 m is a released from rest and at time T equals to zero. The angle made with the vertical is 13 degree. And we need to calculate the angle position of the pendulum at time. T equals to 0.35 2nd. And at time equals two 3.45 seconds. And finally At time equals two six second. No one is all the apart first and it was all this it will be forced calculating the angular speed of the pendulum. And since the speculum is simple pendulum. So oh my God that is, the angular speed is given by under root G. Over L. It's under root G. We have Actually the gravity and its value is 9.8. Media per second squared Divide by L. which is 0.3. And on for the simplification we'll get the answer to be 5.71 radiant purse again. So this is the angular speed where we can easily calculate the angler position of the pendulum at time equals two 0.35 seconds. And it is given by theater. Is the goals. To think they are not times co sign omega teen. So we're gonna plug the valleys here. So take it out. We have 13° times. Cosine omega T. Omega. We have calculated as 5.71 multiplied with tea. So T we have 0.35 2nd. So on. Further simplification will get the answer to be five point a negative 5.39° and her negative signed the notes that the anger position is opposite to the initial direction. So this is the answer for the airport. That means that theater would be something like this, this would be the anchor position, this would be the theater. This negative sign means this is the opposite to the initial position. So this is the answer for the ipod. Next we're going to solve the B. Part. Now in the B part we have to take time to be 3.45 seconds so we can plug T. S. 3.53 point 45 seconds rest remain as it is. So three to will be period out we have a 30 degree Times. Cosine Omega. We have 5.71 multiplied with tea. So T. V. have 3.45. And on simplification Will get the answer to be 8.58°. Therefore the 3 to in this case will be 8.58°. Next we're going to solve the C. Part where time becomes six seconds so you can plug T. S. Six arrest things will remain as it is today equals theater dot we have 14 Because sine omega we have 5.71 Multiplied with T. We have six and on simplification will get the answer to B -12.42° and Harold to this negative sign the notes that the position is opposite to the initial position, So I hope you got a problem. Thank you.

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