# WAVES AND OSCILLATIONS BY BRIJLAL PDF

principle, oscillations with one degree of freedom, resonance and sharpness of measurements, wave velocity and group velocity, Maxwell's equations. waihisitora.gq - Free principle, oscillations with one degree of freedom, resonance and. waihisitora.gq Harmonic oscillators, linearity and superposition principle, oscillations with one degree of freedom.

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View Test Prep - waves-and-oscilations-by-brijlal-n-subrahmanyam-www- waihisitora.gq from PHYSICS 01 at Jawahar Navodaya Vidyalaya. of Waves And Oscillations Second Edition By Brijlal By waihisitora.gq Studio absolutely free. We give the downloading and install media like a pdf, word, ppt, txt. time waves and oscillations second edition by brijlal pdf is available at our online library. with our complete resources, you could find waves and oscillations.

Many new topics have been included in the text. The subject matter is divided into twelve chapters. Each chapter is Self-contained and is treated in a comprehensive way. Using the S. Solved numerical problems in S.

The book is intended to be a textbook for the undergraduate students of Indian Universities. He has a teaching experience ol'ovcr forty years and has had numerous Research Papers publishccl in outstanding Journals. He has been teaching in this college for the last thirty three years and has written several textbooks in collaboration with N. ISBN Rs. He has a teaching experience ol'ovcr forty years and has had numerous Research Papers publishccl in outstanding Journals.

He has been teaching in this college for the last thirty three years and has written several textbooks in collaboration with N.

ISBN Rs. Introduction In every day life we come across numerous ttiings that move. These motions are'of two typgs;. The first type of motion of a body about a mean position is called oscillatory motion. A moving train, flying aeroplaire, moving ball gtc. Examples of oscillatory motion are: Sometimes both the types of motion are exhibited in the same phenomenon depending on our point of view.

The sea waves appear to move towards the bcach but the whter moves up and down about the rnean position. When a stretched. Simple Harmonic Motlon kt Y P bG a particle moving cin the circumference of a circle of radius a with a uniform vetocity u Fig. The circle along which P moves is called the circle of refercnce.

As the particle P moves round the circle continuously with uniform velocity, lhe foot of the perpendicular M, vibrates along lhediameter l'l'. If the motion of Pis uniform, then the motion of M is periodic i. Fmm the LMPo,. Tlre maximum displacemenl of a vibrating particle is cdled its cmplibde. U Tlre -tc sign shows tltlr t' direction of the acteleiation and forcc are opposite to the direction of mo ion of the virkating parricle-.

I Catcilate i ,nrt iiiit riuc pe riul 'Thc vckrity of a Jxrriclc crr: Exemple Show that for a panicle executiitg SHM, tlu instantaneous bxamplc 'tl. A prticte ercculrr sinde The phase differcncc. Exampte Write down the equation lor a wave travelling along the negative Z direction and having an omplinde O0l m,frequency 5S0Hz and speed jjO mls.

How v,ould thc equation change if a wave with thc same Nraneters v'as travelling along the positive zdirection. Justify youranswer. Example l,ll. Show that the mean kine. A pendulum of a ckrck, a loadcd spring and LC circuit have qrc degrec of fieedom.

In tlre case of simple pendulum, rhe swing dcpnds ryofi fte ingular diryraccnrcnt mqde hy thc string wirh rhc vcrtical direction.

## (Second Revised Edition)

In rhe dse of a loaded spring, thcdispLilerncntof lhc mass, and inrhc casc otLC circuit thechargeon rhe c'rrdcnscr plarc describcs the nmurc of rhc oscillarions Fig.

Tlrese dcillaions! All thcsc svstems hale one degree of freedorn. An ideal simple pendulum should consisl of a heavy particle suspended by means of a weightless, inextenisble, flexible string from a rigid support. Suplnse at any instant of time r, it is at i.

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Resolve Mg into two rcctan-. When A. C etc.. Hcnce supcrpositioo principb b tnre only in thi cosc of homogereous lincar equations. Also the sum of any two solutions is also a solution of thc homogencous linear cquation. In rhe case of a simpte pndurum, if rhe size of rhe bob tBob of is largc, a corecrion has to be apptied. This point is-called the point of sr;spension.

In Fig. At rhis positioq rhe. Lct th rmmcor of insria of drc pardfrrn fun m aiis passing thorrgh Safid p. Here L is the distance between the two knife edges. Equarion 9 is similar to the equalion of a simple pendulum. When the posirions of Kr.

Kz Mt, Mz and M3 are linally adusted, ihe time periods about each knife edge must be equal. The positions of Mr, lhen ,,: Mz and Mr must be'the same while determining the time period abolt,erch knife edge. One end of the qpring Sr is attached ro a rigid walt at A and the. Consider two springs each having a length ao in ttre free relaxed position.

It is ta 1. The length of each spnng in the horizontal l6ig. This tension acts along the axis of the spring.

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The component along thc Y-aris contributes ths return folpe and the transverse oscillations are set up in the system: The return folce for each spring is Isin 0. A slinkf is q. In srinky approxinration. In rhe equiriu.

The dishnce is per unit displacemenr of the spring bc K. A body suspended from thc balance oscillates with afreqwn y oI'. Knowing the values pf M,andf, the varue oi rcan be carcutared.

Detcrmlnation of K. To'detenlur' the iarue of tension per unit dispraceof thgspring, a sma[ mass m is airached ro the free end rpri"i. This eguation is similar to ge eguation of simpte -harmonic ,ri motion,'. A spring is hun!

Calculate i 1he ting period and i,i i the frequency of oscillatiott, When the spihg is'lahded with I00 grams r? In rhe equiribium iJ. When rhe mass is dispraced downwardi and [fr,'i;;;-ii'ia; ,irpr". Knowing the values pf M,and K, the value otf T canbe catcutated. Detormlnotion of'I Tg'derermirc the iarue orr"nrion p. I-et it. This equation is similar to 3he equation of simple -harmonic 'rl motion,' gy.

Calculau I dllgwed.

## Waves and Oscilations by Brijlal n Subrahmanyam Www Euelibrary Com

The distance per unit displacemenl of the spring be K. Hfr calri'u il;: The of onc pcoeilrrnr.

Discuss the LC circuit and catculate the. Discuss the two normal modes of oscillations to gravity using will you determine the value of acceleration due. Discuss the case of simple harmonic oscitlations between two linear sPrings' loaded spring is Show that rhe time period of osciltation of a t. Etluations ,r and xfr represent 0re angular. Calculate the average kinetic and rhe total energy "n"rgy erecuting si. Give examptes of the systems that oscillate with qne degree of freedom. Explain the term damped oscillations.

Obtain the expression for thb time period of a simple pendulum. AIso dcrive the expression for the time. A simple periodic wave dislurbance with in the positive x direction' At a given instant'. If rhe iisplacements of the vibrating partifle are considered along the y-axis, the individual displacements are given by. Composition oiTwo Simple H"ti9ry: This represents the general equation of an bllipsc. Thus, due ro the super imposition of two sirnple harmonic vibratipns, the displacement of the particle will be along a curve Fig.

Figure 2. This reprcsents the equation of rhe sraight line. SD Fig.

Graphical method. Draw two circles of reference with centres Cl and Cz and radii a and b respectively. Divide each circle into eight equal parts, markcd O, 1,2,. The angular frequency in each case is to. Similarly, if the particle O is subjected to the simple harmonic motion along the Y-axis onl! Divide each circle into eight equal parts, marked'0,.

## Text book of sound brijlal and subrahmanyam

I-ei a particte be influenced simultaneously by two. Thelwo ions at right ingles to. When the particle O is subjected to the two simple harmonic motions simultaneously ; ttro rcsultant vibration of O will be alons: At zero, zero position, the particle is at. After 78 seconds, conesponding to l, I position in each circle, the particle will be at B.

After Tl4 seconds, correspondin gto2,2positions in each circle, the particle will be at P. Tlie points on the circle of rcfercnce anr marked showing that tlrcre is a phase difference ol'. SimilarlyC, O, E,. The angular frequency and time perid remain the same as for the two con-.

If a particle is mciving along a circular path of radius c with angular frequency or, lt can bc considered to be undef thl influence of two rectangular SHMs having equatr amplitude of value a and angulzu frequency ot, and a phase differencc of n l2. The phase difference tretwecn the two vibrations is cFrom equation 2. Divide the circle paIts.

Similarly, if the particle O is subjected to the SHM along the f-axis only, the partiile will vibrate alongyy'. After equal inrervals of time the positions Ii, C, O etc. The anirolitude of swing decreases continuously with time and finally thi oscillavibrations are called-free dsmPcd vibrationi'.

This is only an ideal case. Int thJfirst chapter, for the motion of a pendulum, spring, LC circuit erc. In such cases therc is no ims of enprgy by friction or otlrcrwise. The amplilude of swing remains constant. Tlie time period of osqi[dion dcecnds onty on. The pendulum will coritinue to oscitlate with the. SIry-I io sn Electrical Ctrcuit In thc case of an elecrical ciicuit, the force equation is reptaced by the voltage equation. A condenser of cqacity t uF, an inductance of0.

Is the circuit oscillatory? Forced Vibrations ilirmonic motion depends on a Thetime penod of a body: In the case of free vibratiohs the solution is. The oscillations will maximum amplitude and this starc of'vibration of a syslem is callcd lt means that, wtlcn lhc forced frequcncy is equal Eo the natural 'of vibration of thc body, resonance takes placc. If ftiction is prescnl. Resonance and Sharpness of Resonance In the case of forced vibrations, the general solution frir the displacement at.

It means that the response R is inversely proportional to the'frictional lbrce.

## Waves-and-oscilations-by-brijlal-n-subrahmanyam-www-euelibrary-com.pdf

In the adsencgof friction, the response is maximum-'. For curve A, p is large and for curve C, p is less. The response decreases for values ofplto greater than. In thg case of the resonance tube, the damping force is largd and the'graph be similar to the curve A in Fig.

In this case the sharpness of resonance is maximunt"'ln a very narrow region.

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Even a slight variation in length or tension reduces the sharpngss considerably. The vibiations die out rapidly. Thus, the results obtained with a sonomiter are accurate. Phase of Resonance Considering the phasc lead of the forced vibrations with rctbrcnce re the. Diicuss rhc phcnomenon of sharpnass of resonance and show how it Kanpur, dcpcnds on thc damping factr. Give the theory and discuss the condition of rcsonance.

Discuss the effect of IDelhi Sub; Supp. Wht is a fqcd vibration? Discuss when subjected to motion harmonic simple damped aystem cf,ccuting of.

Dcfine quality factor and bandwidth of the sharpness of Obtain quality factor for a driven harmonr". Explain, in brief, 0 free oscillations, i0 forced oscillation and rir phcnomenaof. Wnat Oo you understand by dam vibrations?Core physics iii properties matter and sound.

A moving train, flying aeroplaire, moving ball gtc. Ph2b01u mechanics and properties matter. Cancel Yes. These campressions and rarefactions travel forward atong the wave and transfer enrgy in the direaion of propaga-.

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