Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

(II) $(a)$ Determine the equation of motion for $\theta$ as a a function of time) for a torsion pendulum, Fig. 18 , and show that the motion is simple harmonic. $(b)$ Show that the period $T$ is $T=2 \pi \sqrt{I / K}$ . [The balance wheel of a mechanical watch is an example of a torsion pendulum in which the restoring torque is applied by a coil spring.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

a. $$\theta=\theta_{0} \cos (\omega t+\phi), \omega^{2}=\frac{K}{I}$$b. $$T=2 \pi \sqrt{\frac{l}{K}}$$

02:55

Shital Rijal

Physics 101 Mechanics

Chapter 14

Oscillators

Motion Along a Straight Line

Motion in 2d or 3d

Periodic Motion

University of Michigan - Ann Arbor

University of Washington

Hope College

University of Sheffield

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.

04:03

(II) A physical pendulum c…

06:48

A mass of 0.50 kg hangs fr…

01:19

The pendulum oscillates ab…

02:59

The balance wheel of a wat…

01:24

A simple pendulum is a sma…

04:42

$\bullet\bullet\bullet$ Th…

in this problem on the topic of oscillators, we are asked to determine an equation of motion which is data as a function of T. For a torsion pendulum as shown in the figure, were then asked to show that the period of oscillations T. Is two pi times the square root of I. O. K. Now from the text, we are given that the talk of italian pendulum tour is equal to minus K. Peter where K. Is a Tory in constant. And from Newton's second law of rotation, we know that the some of the talks sink. My tour must equal to the moment of inertia. I find the angular acceleration alpha, which we can write as. I times G. Two theater. Bye. T. T squared. Now we assume that the talk applied by the twisting of the wire is the only talk. And so I. D to d to D T squared is equal to minus K. Peter. So we've set up the differential equation of the form D. Two data. T T squared is equal to minus. Okay? Over I times peter which we can right as minus omega squared times theater. So here we have a second order differential equation and this is the second order differential equation for simple harmonic oscillation. And so we know the emotion needs to be simple harmonic reunite the solution to this equation. We get, peter is a function of T. Is equal to peter not call sign or make a T. Plus if I. And hence we have an equation of motion body to in terms of time where omega squared is K. Oh I now that we have our equation of motion, we want to find the period of motion and the period of the motion is found from the angular velocity. So we know omega squared is K over I. Which means that omega is simply the square root. Okay. Of I. We know omega is also two pi over the period teeth. So by rearranging we get the period T to be two pi times the square root of I over K as required.

View More Answers From This Book

Find Another Textbook

01:29

Richard was mad at his sister so he took her iPhone and dropped it out the w…

03:36

A wrecking ball is being used to knock down a building. One tall unsupported…

02:16

A man bought a lot worth Php 1,000,000 if paid in cash. On the installment b…

01:23

A Gi.I pipe lining material of silicon carbide used in the conveyance of pul…

02:10

A crane does 62,500 Joules of work to lift a boulder a distance of 25.0 mete…

01:57

How long does it take to accelerate a car from a speed of 50 km/h to a speed…

02:42

A ball is thrown upward at an angle with a speed and direction such that it …

02:21

If your eye has an uncorrected focal power of 50 diopters, and an object fo…