Simple harmonic motion Questions and Answers

300 N m connects two blocks having masses 2 kg and 3 kg lying on a smooth horizontal plane If the spring block system is released from a stretched position find the number of complete oscillations in 2 seconds Take 10 A spring of force constant k

A 2 kg block moving with 10 m s strikes a spring of spring constant N m attached to 2 kg block at rest kept on a smooth floor The time for which rear moving block remain in contact with spring will be 10 m s 2 kg O 2 S L 1 s S oooo 2 kg

A small ball of mass m 4kg is affixed at one end of a light rod of length 10cm the other end of which is hinged to a fixed pivot on a wall One end of a spring of force constant k 100 is attached on the rod at a distance d 1cm from the hinge and the oth end of the spring is attached to a nail on the wall In equilibrium the rod stays horizontal an angle between the spring and the rod is 0o 30 If the ball is pulled downwards and releas the system begin to oscillate Find time period of these small amplitude oscillations B F O 2TT 4TT 8TT 16TT 18 0000000000

The springs in figure A and B of same material are identical in shape but length in A is three times each of that in B The ratio of period A B eeeeee m O 3 1 3 O 3 eeeeeeee eeeee TA TB hr min is

When a particle perform simple harmonic motion then its O Velocity continuously change and acceleration remain constant Velocity and acceleration change continuously Velocity remain constant and acceleration continuously change O Velocity and acceleration does not change

In SHM when a particle passes through its mean position then particle s speed and acceleration O Speed minimum Acceleration maximum Speed maximum Acceleration minimum but non zero Speed minimum Acceleration minimum Speed maximum Acceleration zero

1 kg block performs vertical harmonic oscillations with amplitude 1 6 cm and frequency 25 rad s The maximum value of the force that the system exerts on the surface is 11n N Value of n is g 10 m s n 10 1 kg 0000

Speed of a particle executing SHM is v at mean position The speed of the particle when its 1 displacement from mean position is equal to th of 4 the amplitude of the motion is Ov 1 4 15 4 17 4

40 Which of the following does not hold in SHM 1 Work done in one complete oscillation is zero 2 Energy is converted continuously from PE to KE and vice versa 3 Acceleration is maximum at the mean position

The spring shown in the figure is unstretched when a man starts pulling the block If the man exerts a constant forces F the maximum elongation in spring is AC K E 1 5 plain de her aon of mon

3 A body describing S H M has a maximum acceleration of 8 m s and a maximum speed of 1 6 m sec its time period should be 1 0 8 sec 2 0 4 sec 3 0 2 sec 4 0 1 sec

3 4 15 A particle executes SHM along x axis with amplitude A and mean position at x 0 If it starts from negative extreme its equation of motion is 1 x A sincot 2 x A cosent 3 x A sinoot 4 x A cosex

Kimum at mean position Velocity is maximu For a particle undergoing SHM the velocity is The curve will be plotted against displacement 1 a straight line 3 a circle The 2 a parabola 4 an ellipse inh of

19 When a particle oscillates simple harmonically its kinetic energy varies periodically If frequency of the particle is f the frequency of the kinetic energy is 1 f 2 2 f 3 2f 4 4f A heavy brass sphere is hung from a spring and 20

A positively charged pendulum is oscillating in a uniform electric field as MAMAMA shown in the figure Its time period as compared to that when it was uncharged A will increase C will not change YST Jobs w D will first increase and then decrease will decrease

33 The equation of SHM of a particle is given as 2x 32x 0 where x is the displacement dt from the mean position of rest The period of its oscillation in seconds is 1 4 2 KIN 2 2 4 2n

14 a How long after the beginning of motion is the displacement of a harmonically oscillating point equal to one half its amplitude if the period is 24 sec and initial phase is zero 1 12 sec 2 2 sec 3 4 sec 4 6 sec

A rod of mass 2m length is hinged at one end A on a horizontal friction less table at another end B a spring of spring constant k is connected as shown in figure Then angular frequency of rod for small oscillations is reeeeeee WA

lators of equal mass are oscillating about the origin with angular frequencies and 2 and have total energies E and E2 respectively The variations of their momenta p with positions x are shown in the figures If n and a b n then the correct equation s is are A E 00 E 002 C 00 n b P Energy E a X P Energy E 2 n 0 R D E E 00 02 R X 61 2015

A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface The block oscillates with small amplitude A about an equilibrium position Xo Consider two cases i when the block is at xo and ii when the block is at x xo A In both the cases a particle with mass m M is softly placed on the block after which they stick to each other Which of the following statement s is are true about the motion after the mass m is placed on the mass M 2016 A The amplitude of oscillation in the first case changes by a factor of whereas in the M m M second case it remains unchanged B The final time period of oscillation in both the cases is same C The total energy decreases in both the cases D The instantaneous speed at xo of the combined masses decreases in both the cases

7 The ends of a rod of length I and mass m are attached to two identical springs as shown in the figure The rod is free to rotate about its centre O The rod is depressed slightly at end A and released The time period of the oscillation is

A stepped pulley nang mass m redius o gyration k is connected with two ideal spring of stiffnesws k and k as shown in figure I the pulley shown in the figure If the pulley rolls without sliding find the angula frequency of its oscillation k 000000 k 000000 5 R H A AI

70 A uniform disc of radius R is pivoted about point p such that it is free to oscillate in the vertical plane Distance between the pivot and centre of disc x such that the time period of oscillation is minimum R is Value of n is vn P

neet prep by strings at A and B If the mass M is displaced slightly 4 T 2T Ts out of this plane and released it will execute oscillations with period Given AM BM 1 AB 2d A 1 2T 2 2 9 L d 2 M Oscillations and Waves Contact Number 9667591930 8527521718 11 The transverse displacement y x t of a wave on a string is given by v x t e as be 2 ah st This represents a 1 wave moving in x direction with speed 2 standing wave of frequency b 3 standing wave of frequency 4 wave moving in x direction with speed 12 1010

1 Two particles are executing S H M of same amplitud and frequency along the same straight line path The pass each other when going in opposite direction eac time their displacement is half of their amplitude What i the phase difference between them 1 5 6 2 2 3 3 3 4 6

6 A particle of mass m is attached to three springs A B and C of equal force constant k If the particle is pushed a little towards any one of the springs and left find the time period of its oscillations topo m Felle 1 2 m k 2 2x 2m k 3 2 m 2k 4 2 m 3k Fele

9 A Textbook OF APPLIED PHYSIC positiv TELANGANA STATE 2 5 c If the period of S H M is 6 second and amplitude is 5 cm what is the displaceme at a time 7 second after the passage of the particle through its extreme p displacement what is the maximum speed of a particle executing of S H M with a time perio TL 4 and amplitude 7 10 2 m 56 x 10 ms 11 The particle is executing S H M with acceleration 64 x 10 2 ms2 and displacemen 4 x 10 2 m What is its time period TC 12 second 12 A particle of mass 10 gram is describing S H M along a straight line with a period of 2 second and an amplitute of 10 cm When it is 2 cm from its equilibrium position 480 m erg what is its kinetic anera

3 Block is in equilibrium initially Now we displac the block by a distance 0 4 m downward and the release Find time taken by the block to reach t natural length of the spring 1 2n 3 2 2 2 100 3 1 2 100 T 2 100 2 K 100 N m 2kg

xiii Electrons in an oscilloscope are deflected by two mutually perpendicular fields in such a manner that the displacement at any instant is given by x 4 sin wt 6 and y 4 sinwt Find the nature and equation of the path

A particle of mass 3 gm moves along the x axis and is attracted towards the ongin by a force whose magnitude is numerically equal to 12 times the instantaneous displacement from the ongin The particle is also subjected to a damping force whose magnitude is 12 times the instantaneous speed If it is initially at rest at x 10 cm which one of the following equations gives the particle s position at a later time t 10 e cos 4t 10 40t e t 10 20t e 2 10 e 21 sin 4t

Match the following COLUMN 1 COLUMN II COLUMN I A Time period of infinite pendulum B The period of a simple pendulum in a satellite C Time period of oscillation of particle in SHM COLUMN II P Time period of a physical pendulum pivoted at its CM Q Time period of a body in a smooth chute made inside the earth R Time period of second s pendulum D Time period of S Half of the time period of loscillation is equal loscillation of kinetic energy of

I wo positive charges each of equal magnitude q are placed at a separation 2a perpendicular to X axis Another negative charge of mass m is placed midway between the two charges on X axis If this charge is displaced from equilibrium state to a distance x x a then the particle 1 will execute simple harmonic motion about its its equilibrium position 2 will oscillate about its equilibrium position but will not execute simple harmonic motion 3 will not return back to the equilibrium position 1 1

dwhen xa 9 A particle in SHM is described by the displacement function x t A cos wt 0 If the initial t 0 position of the particle is 1 cm and its initial velocity is ncms 1 what is its amplitude The angular frequency of the particle is a 1 cm c 2 cm b 2 cm d 2 5 cm 10 Two springs with spring constants K 1500 N m and K 3000 mar force The ratio of potential ETPHYSI

The time periods of the hanging bobs in figure i and ii for their simple harmonic oscillations in vertical planes are T and T respectively Then a the T T2 value of a is 1 30 21 21 ii 1 O0010 O O O O O O O

Two bodies of masses 10 gm and 90 gm are connected by a weightless spring of length 10 cm Find the force constant of the spring if the frequency of oscillation of the system is 53 Hz Ans 1000N m

A circular disc suspended from a torsional wire oscillates with a time period T when twisted by a small angle 8 from equilibrium and released I If another disc of same material but twice the radius and one fourth thickness is made to oscillate alone with same wire its time period is found to be nT Write the value of n

Pre Medical Physics The period of oscillation of simple pendulum of 16 length L suspended from the roof of the vehicle which moves without friction down on an inclined plane of inclination a is given by 1 2n L Vgcos a 3 2T L g 2 2 4 2 L g sina L gtan a

Two pendulums of length 1 21 m and 1 0 m start vibrating At some instant the two are in the mean position in same phase After how many vibrations of the longer pendulum the two will be in phase 1 10 4 21 2 11 3 20

3 S 5 5 x m A block is resting on a piston which executes simple harmonic motion with a period 2 0 s The maximum velocity of the piston at an amplitude just sufficient for the block to separate from the piston is g 10 m s 1 1 57 ms 1 3 1 ms 1 2 3 14 ms 1 4 6 42 ms

A simple harmonic oscillator consists of a block attached to spring with k 200 N m The block slides on a frictionless horizontal surface with equilibrium point x 0 A graph of the block s velocity v as a function of time t is shown Correctly match the required information in the column 1 with the values given in the column II use 10 Column l V m s 2x A The block s mass in kg B The block s displacement at t 0 in metres C The block s acceleration at t 0 10 s in m s D The block s maximum kinetic energy in O 21 PUUSU p q s t 0 10 Column II 0 20 200 0 20 0 4 4 0 0 20

Two simple harmonic motions are given by x a sin wt a cos wt and x1 cos wt The ratio of the amplitudes of the first to the second and th 3 x2 x a sin wt phase difference between them respectively are OVE and and I and 2 12 and 2

A particle executes simple harmonic motion Let P be a point near the mean position and Q be a point near an extreme The speed of the particle at P is largem than the speed at Q Still the particle crosses P and Q equal number of times in a given time interval Does it make you unhappy

4 Q 0 W 0 164 A particle executing SHM crosses points A and B with the same velocity Having taken 3 s in passing from A to B it returns to B after another 3 s The time period is 1 15 s 2 6s 3 12 s 4 9 s

A particle of mass m is subjected to a force F at bx i initially the mass lies at the origin at rest Here x refers to the x coordinate of mass t refers to the time elapsed All the values are in SI units i e F m t x a and b Take m 1 kg a 1 N s b 1 N m Now match Column I with Column II Q 16 1 Maximum velocity attained by the particle Correct answer

Two particles are in SHM in a straight line about same equilibrium position Amplitude A and time period T of both the particles are equal At time t 0 one particle is at displacement y A and the other at y A 2 and they are approaching towards each other After what time they cross each other 1 T 3 3 ST 6 2 T 4 4 T 6 10

23 A constant force produces maximum velocity V on the block connected to the spring of force constant K as shown in the figure When the force constant of spring becomes 4K the maximum velocity of the block is a V 4 c V 2 k mormor m b 2V d V

21 The angular frequency of a spring block system is wo This system is suspended from the ceiling of an elevator moving downwards with a constant speed vo The block is at rest relative to the elevator Lift is suddenly stopped Assuming the downward as a positive direction Then a The amplitude of the block is Vo o b The equation of motion for the block is c Both are correct d Roth VO vo sin wot o

22 A small ball of density po is released from rest from the surface of a liquid whose density varies with depth has p a h Mass of the ball is m Select Po 2 the most appropriate one option a The particle will execute SHM b The maximum speed of the ball is 2 23 c Both a and b are correct d Both a and b are wrong Here a and are positive constants of proper dimensions with a 2

Two blocks A and B of mass m and 2m respectively are connected by a massless spring of spring constant K This system lies over a smooth horizontal surface At t 0 the block A has velocity u towards right as shown while the speed of block B is zero and the length of spring is equal to its natural length at that instant In each situation of list 1 certain statements are given and corresponding results are given in list II Match the statements in list l corresponding results in list II F mg List I P The velocity of block A Q The veloicty of block B R S The kinetic energy of system of two blocks The potential energy of spring P 20 2R 1S 3 CP 30 1 R 1S 2 P 30 1R 3S 4 P 20 28 18 4 List ll 1 Can never be zero 2 3 4 may be zero at certain instants of time B 2m is minimum at maximum compression of spring is maximum at maximum extension of spring mm m smooth horizontal surface U 4

SolveLancer TestJA modified U tube is made of uniform cross section as shown in figure U It is filled with fluid of density S The mass of fluid is m Total length of the fluid is l and area of cross section is uniform If liquid is slightly displaced find the time period of oscillation SolveLancer Test a A 1 COS T 1 cos b B 2 d D sin 6 1 1 sin 0 c C 2 1 sin 8 0 1 2