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Review Questions

Simple harmonic motion

1. A particle undergoes SHM with an amplitude of 4.0 mm and angular frequency of 2.0 s -1. At

t 0! the displacement is mm. "rite down the equation gi#ing the displacement forthis motion.

2. A particle undergoes SHM with an amplitude of $.00 cm and an angular frequency of 0.2%0

s-1. At t   0! the #elocity is 1.24 cm s-1

&a' "rite down the equations gi#ing the displacement and #elocity for .this motion.

&(' )alculate the initial displacement.&c' )alculate the *rst time at which the particle is at + 2.00 cm and + -2.00 cm.

3. The graph in Figure shows the displacement of a particle from

a fixed equilibrium position.

a) Use the graph to determine: (i) the period of the motion (ii)

the maximum !elocit" of the particle during an oscillation

and (iii) the maximum acceleration experienced b" the

particle.

b) #n a cop" of the diagram mar$: (i) a point where the

!elocit" is %ero (label this with the letter &) (ii) a point

where the !elocit" is positi!e and has the largest

magnitude (label this with the letter ') and (iii) a point

where the acceleration is positi!e and has the largestmagnitude (label this with the letter ).

4. ,he graph in igure shows the #ariation withdisplacement of the inetic energy of a particle of 

mass 0.40g performing SHM. /se the graph todetermine

&a' the total energy of the particle 

&(' the ma+imum speed of the particle&c' the amplitude of the motion

%. A particle of mass 0.%0 g undergoes SHM with angular frequency co .0 s-1 andamplitude 3.0 cm. or this particle! determine

a' the ma+imum #elocity

(' the #elocity and acceleration when the particle has displacement 1.% cm and mo#estowards the equili(rium

position from its initial position at + 3.0 cma' the total energy of the motion.

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The simple pendulum

1 State what is meant (y oscillation and simple harmonic motion.

2 State two ways in which an SHM oscillation is dierent from a general oscillation.

3 A (all goes (ac and forth along a hori5ontal 6oor (ouncing o two #ertical walls. 7s themotion an e+ample of an oscillation8 7f yes! is the oscillation simple harmonic8

4 A (all (ounces #ertically o the 6oor. 7s the motion of the (all an e+ample of an oscillation8 7f

yes! is the oscillation simple harmonic8

5 9+plain how you would use a spring of nown spring constant to measure the mass of a (ody

when in a spacecraft in outer space.

6 9+plain why the oscillations of a pendulum are! in general! not simple harmonic. "hat

condition must (e satis*ed for the oscillations to (ecome appro+imately simple harmonic8

7 Show e+plicitly that! if , the period of the motion is gi#en (y

independently of A and ɸ.

8 ,he displacement of a particle e+ecuting SHM is gi#en (y y   %.0cos &2t' ! where y  is inmillimetres and t  is in seconds. )alculate

a the initial displacement of the particle

( the displacement at t = 1.2 s

c the time at which the displacement *rst (ecomes -2.0 mm

d the displacement when the #elocity of the particle is :.0 mm s-1.

9 &a' "rite down an equation for the displacement of a particle undergoing SHM with an

amplitude equal to $.0 cm and a frequency of 14 H5! assuming that at t 0 the

displacement is $.0 cm and the particle is at rest.

&(' ind the displacement! #elocity and acceleration of this particle at a time of 0.02% s.

1A point on a guitar string oscillates in SHM with an amplitude of %.0mm and a frequency of 

4:0 H5. ;etermine the ma+imum #elocity and acceleration of this point

Travellin!"wave characteristics

1. A radio station emits at a frequency of 0.$ MH5. "hat is the wa#elength of the wa#es

emitted8

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is polari5ed! partially polari5ed or completely unpolari5ed! e+plaining your answers.

&a',he intensity of the transmitted light is the same no matter what the orientation of the analyser.

&(' ,he intensity of the transmitted light #aries depending on the orientation of theanalyser. At a particular orientation! the transmitted intensity is 5ero.

&c',he transmitted intensity #aries as the orientation #aries! (ut it ne#er (ecomes 5ero.

4% &a' State Malus=s law.

&(' olari5ed light is incident on a polari5er whose transmission a+is maes an Bingle of 2%C with thedirection of the electric *eld of the incident light. )alculate the fraction of the incident lightintensity that gets transmitted through the polari5er.

5%  olari5ed light is incident on a polari5er whose transmission a+is maes an angle θ with thedirection of the electric *eld of the incident light. Setch a graph to show the #ariation with angleθ of the transmitted intensity of light.

6%  /npolari5ed light of intensity 70 is incident on a polari5er. )alculate! in terms of 70 the intensity oflight transmitted through the polari5er.

7% /npolari5ed light of intensity 70 is incident on a polari5er. ,he transmitted light is incident on asecond polari5er whose transmission a+is is at :00 to that of the *rst. )alculate! in terms of 70 theintensity of light transmitted through the second polari5er.

&nter'erence

1% 9n un e+perimento de interferenciacon dos ranuras! Dstas seencuentran separadas por unadistancia de 0.200 mm! y lapantalla estE a una distancia de1.00 m. Se o(ser#a que la tercerafranFa (rillante &sin contar la franFa(rillante central frente a lasranuras' estE despla5ada .4 mmde la franFa central &*gura '. )alcule la longitud de onda de la lu5 utili5ada.

2% "a#es lea#ing two sources arri#e at point . oint is 12 m from the *rst source and 1:.% mfrom the second. ,he wa#es ha#e a wa#elength of 3 m. "hat is o(ser#ed at 8

03. lanar wa#es of wa#elength 1.0 cm approach an aperture whose opening is also 1.0 cm.;raw the wa#efronts of this wa#e as they emerge through the aperture.

04. Gepeat question 7 for wa#es of wa#elength 1 mm approaching an aperture of si5e 20 cm.

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0%. 7n the corridor shown in igure 4.11 an o(ser#er at point can hear someone at point (ut cannot see them. "hatphysical phenomena may account for this8 How could see 8

0:. ,wo loudspeaers are connected to thesame audio oscillator. An o(ser#er walsalong the straight line Foining the speaers&see igure 4.12'. At a point M halfway(etween the speaers he hears a loudsound. <y the time he gets to point adistance of 2.00 m from M he hears nosound at all. 9+plain how this is possi(le. ind the largest possi(le wa#elength of soundemitted (y the loudspeaers.

0>. A radio station! G! emits radio wa#es of wa#elength 1:00 m which reach a house. H!directly and after re6ecting from a mountain!M! (ehind the house &see igure 4.13'. 7f thereception at the house is #ery poor! what isthe shortest possi(le distance (etween the

house and the mountain8

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