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(II) A uniform meter stick of mass $M$ is pivoted on a hinge at one end and held horizontal by a spring with spring constant $k$ attached at the other end (Fig. 28$)$ . If the stick oscillates up, and down slightly, what is its frequency? [Hint. Write a torque equation about the hinge.

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the frequency of the oscillations of the meter stick is $\left[\frac{1}{2 \pi} \sqrt{\frac{3 k}{M}}\right]$

03:57

Shital Rijal

05:19

Keshav Singh

Physics 101 Mechanics

Chapter 14

Oscillators

Motion Along a Straight Line

Motion in 2d or 3d

Periodic Motion

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser 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.

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(II) A uniform meter stick…

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A mass $m$ hangs from a un…

05:08

In Fig. $15-31,$ two ident…

01:41

A spring with spring const…

03:38

The mass $m$ shown in the …

01:50

A pendulum of length $L$ a…

we have given that one end of a uniform it'll stick is hinge and the other end is connected by a spring in vertical direction and it is told that it oscillates in up and down direction and we have to find the frequency of these oscillations. So first of all, I am growing the diagram for this execution so that this is our meter stick of Marxism and lengthen and it is hinge at this end. And we have given that it is supported by a spring that this is the spring and spring constant. Is that this is scared. And we have given the mosque and lent no. First of all we can see that when this will come in equilibrium positions. So let this point is over and we can say that at equilibrium position. Network about point over B zero. So it or it will be one is due to the weight of this road which is acting at center, this is M Z. And let the extension in this spring is why not initial extension. So we can say that Net told due to the weight is MG into L by two, decision clockwise direction minus came into this is why not into this is an antique localization. So from here we get MG by two is equal to the C. Scale. Why not let this is a question first. Now, I'm going to displace this road, let this is the road. I'm going to show the conditions of this. So this is the initial condition when the equilibrium Harry led the equilibrium at this. The road is in this position and this is the extension in the spring, that is why not. Now I'm going to displace it another displaced by this angle that if this is angle so I'm going to displace it angle twitter and let this extension is why. So we can see that for this small oscillation against a small angular displacement. That is to we can write network about 0.0 is equals two alpha. So network is due to wait that is MG into L by two minus one is spring forth. That is care into white plus why not? And well and this will be I into alpha can be written as day to try to buy data square now further I can simplify this. So this is MGl by two minor disease. Ky l minus K Why not into well physical as to why? A million square by three. And this is day to treat upon data square. Now from equation when we can see that this too will cancel out and finally we will get um many square by trying to the to try to buy duty square will be close to this is minus of care into weil. Now I can see that here. Why can be written as that is why is equals two L. Scientist er and for a small displacement this can be written as why is equals two L into theater. So finally we'll get disease And many square by three. This is the to tee it up on the T square is equal to, this is minus K. Early square into twitter. Now Alistair will cancel out from both sides and we will get this is M by three or I can say this can be written as they took it up on the t square flash. This is tricky but I am And to treat us as equals to zero. This is the second order differential equation and we can say that from here we get the omega duties and wrote of 3K by um this is the value of omega. Now we can see that frequency will be that is Omega by two Pi. So frequency will be one upon to buy. This is a note of three K by M and this will comes or to being hurt. So this is the answer of are given to shin. Yeah, thank you.

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