Simple harmonic motion Questions and Answers

34 A disc of mass m is connect and K as shown Find time period of oscillation All surfaces are smooth K wwwww K wwww

50 The minimum time taken by a body executing simple harmonic motion in which its speed decreases by half its maximum speed will be T time period 1 3 T6 T 12 2 4 T 4 T 0

23 A ring of mass m and radius R oscillate about point O as shown in figure then its time period is 1 2T g 3 T 2R g 2 8R g ash Tower 8 Pusa Road New Delhi 110005 Ph 011 47623456 R 2g 4 T

10 A stiff spring k 666 N m has be attached to the floor vertically A mass of 6 66 kg is placed on top of the spring as shown below and it finds a new equilibrium point If the block is pressed downward and released it oscillates If the compression is too big however the block will lose contact with the spring at the maximum vertical extension Draw a free body diagram and find that extension at which the block loses contact with the spring

The displacement of a particle in meter from its mean position is given by the equation y 0 2 cost sin The motion of the above particle is 1 not simple harmonic 3 simple harmonic with the period double that of a seconds pendulum 4 simple harmonic with amplitude 0 4 m The escape velocity from the earth is about 11kms The escape velocity from a planet having twice 2 simple harmonic with amplitude 0 2 m

A simple pendulum with a metallic bob has a time period 10 s The bob is now immersed in a 1 3 non viscous liquid of density bob The time period of the same pendulum becomes 1 10 s 10 3 S that of metallic 10 2 4 10 3 s 2 S

A uniform vertical electric field E is the space between two large parallel plates A small conducting sphere of mass m is suspended in the field from an insulating string of length L If the sphere is given a positive charge q and the lower plate is positively charged then the period of small oscillations of this pendulum is 25 5 g 1 2T 3 2T L qE L moq E 2 2 4 2 g JE L qE m L OF 27 2

Two particles each performing their respective SHM with same amplitude along the same line start their motion from their common mean position in opposite direction If the frequency of oscillation of one particle is 2 Hz and that of the other particle is 4 Hz then the time after which the particle cross each other is

The graph shows the variation of displacement y of a particle executing SHM with time t Choose the correct statement T 2 ben 13T 4T T 4 Question Type Single Correct Type 1 The force is zero at time 3T 4 2 The velocity is maximum at time T 2 3 The acceleration is maximum at time T

A body performs SHM along the straight line segment ABCDE with C as the mid point of segment AE A and E are the extreme position for the SHM Its kinetic energies at B and D are each one fourth of its maximum value If length of segment AE is 2R then the distance between B and D is A B C D Question Type Single Correct Type 1 VSF 2 R 2 3 3R E 1

Starting from the origin a body oscillates simple harmonically with a period of 2s After what time will its kinetic energy be 25 of the total energy Question Type Single Correct Type 1 2 3 1 6s 1 4s 1 3s

stra P O if the time period of the motion is T then its kinetic energy at P be half of its peak value of O if the time taken by the particle to travel from O to P is Question Type Single Correct Type A par 1 2 3 1 2 2 T

SolveLancer Test In the figure given below the two masses were moving same velocity v in same direction and the spring is in its natural length An impulse J 2mv is given towards left to mass A Then how many of given statements are correct The ground is smooth and the spring constant is k VI B m ooooo m a 1 b 2 V A m 1 Mass A stops and Mass B continues to move II The velocity of masses w r t centre of mass change with time after the impulse is given to block A III The masses oscillate about a fixed point with T 27 2k IV Amplitude of oscillation of masses is A v 2k SolveLar So eLancer Test

A 200 g block hangs from a spring with spring constant 10 N m At t 0 s the block is 19 cm below the equilibrium point and moving upward with a speed of 137 cm s What is the block s distance from equilibrium at t 1 0 s Express your answer to two significant figures and include the appropriate units Enter positive value if the block is above the equilibrium point and negative value if the block is below the equilibrium point View Available Hint s

Bob of a simple pendulum has mass 1 kg and charge do Tension in the string doubles when another charge qo is fixed at position Pas shown Time period of simple pendulum for the small oscillation is ns another charge qo remains fixed at P Find value of n g n 1 6m 1 6m Answer 00 01 02 03 04 05 06 07 8 09

Column 1 represents some systems in which the mass is released for rest with spring relaxed All contact surface are smooth strings light inextensible and pulleys light and smooth Colum 2 contains amplitude of small oscillations and colum 3 contains time penod for the oscillations Column 1 Column 2 e 1 111 IV E E 30 9 m 30 e 30 0 D iv mg 2k mg k 2mg k mg 8k P 2 K k 0 1 Column 3 2m R 41 S 21 20 1E1 m Ex m LEIK

Two waves have the frequency of 600Hz one is set at its maximum value whereas the other at zero the phase difference between them will be a 90 degree b 0 degree c 90 x 600 x 50 degree

perrous ure te bus respecur tich pine uffference after var 8 A particle moving in XY plane has a displacement x a coswot along X direction and y b cosawt along direction Show that the trajectory is repeated only if a is a rational number

One cm on the main scale of vernier callipers is divided into ten equal parts If 20 divisions of vernier scale coincide with 8 small divisions of the main scale What will be the least count of callipers 1 0 06 cm 2 0 6 cm 3 0 5 cm 4 0 7 cm

A pendulum clock is set to give correct time at the sea level This clock is moved to hill station at an altitude of 2500 above the sea level In order to keep correct time of the hill station the length of the pendulum O Has to be reduced O Has to be increased O 00 25 Needs no adjustment

Out of the following functions representing motion of a particle which represents SHM 1 y sinot coswt 2 y sin wt 3 t 3 y 5cos 30t 4 4 y 1 wt w t a Only 1 Te b Only 4 does not represent SHM c Only 1 and 3 d Only 1 and 2 2011

The displacement of harmonic simple motion by y A Asinot Bcosoot Then the amplitude of its oscillation is given by a A B c A B particle executing is given b A A B d A B

3 A uniform spring of length L mass m and force constant k is hung from a rigid support and is loaded with a mass 5 m at its lower free vibration of the loaded mass is 3 2 m k 2 m 2k

A particle of mass m is performing the linear simple harmonic motion Its equilibrium is at a 0 force constant is K and amplitude of SHM is A The maximum power supplied by the restoring force to the particle during SHM will be A K2A m 3 2K 2 A m

The kinetic energy of a particle executing S H M is 16 J when it is at its mean position If the mass of the particle is 0 32 kg then what is the maximum velocity of the particle 1 5 m s 2 15 m s 3 10 m s 4 20 m s

A particle performing S H M starts from mean position The position of particle from its mean position where the difference of K E and P E is zero is Take maximum displacement of particle is 8 m 1 2 m 3 4 2 m 2 2 2m 4 2m

0 Two bodies performing SHM have same amplitude and frequency Their phases at a certain instant are as shown in the figure The phase difference between them is x x 1 3 50 R M 2 2 3 2 J 2 9 2 3 2 L 2 T x x 4 None of these

A particle executes linear SHM with a time period of 10 s Find the time taken by the particle to go 1 directly from its mean position at t 0 to 2 amplitude O O 2010 215 60 6 S S 1 2 s of its

0 Two particles P and Q describes simple harmonic motion of same amplitude a same frequency f along the same straight line from the mean position The maximum distance between the two particles is a 2 The phase difference between the particle is 1 Zero 3 B C T 2 4 E N 2 E M T

A horizontal spring block system executes SHM x A sin mot 6 with amplitude A 10 cm initial phase 6 0 and angular frequency The mass of block is M 25 kg and there is no friction between the block and the horizontal surface The spring constant is 2500 N m At t t1 sec for which cot 30 A mass m 75 kg is gently put on the block Assume that collision between the block and the mass perfectly inelastic and mass m remains stationary wrt the block M always 60080880 m M Mean position

80 A ring is hung on a nail It can oscillate without slipping or sliding i in its plane with a time period T and ii back and forth in a direction perpendicular to its plane with a period T2 The ratio T T will be 5 Sept 2020 Evening A C 2 3 2 3 B D 5 w w 5 2

A block Q of mass 2m is placed on a horizontal frictionless plane A second block of mass m is placed on it and is connected to a spring of spring constant K the two block are pulled by distance A Block Q oscillates without slipping The work done by the friction force on block Q when the spring regains its natural length is A KA 3 I T C KA 2 2 B KA 3 D KA 4 K moooo P Q

ase by fo A 0 50 kg object is attached to a vertical spring of constant k as shown above The object is pulled down and released The pject oscillates vertically If up is the positive direction the position x of the object as a function of time is given by the formula x sin ar p where 0 20 m 4 0 rad s and p 7 3 rad 27 Secto mail com A 4 0 s B 3 1 s C 2 0 s D 1 6 s E 1 1 s The period of the oscillation for the object is most nearly dabad HR andia Object m 0 50 kg BAT AP usives x A 8 0 m s B 6 4 m s C 3 2 m s 28 The magnitude of the maximum acceleration of the object as it oscillates is most nearly

1 A particle is executing simple harmonic motion along x axis with a time period T and displacement amplitude A Find the time taken by the particle to move from A 3 to A 3 through the extreme position

A block of mass m hangs from three springs as shown in the figure If the mass m is slightly displaced downwards the time period of oscillation will be 3K elle 3K 2 TA 2T elle m 29K 2T m 3K 12m 19K 13m 2K m 2K

The centre of a solid sphere of mass m and radius R placed on a rough horizontal plane is connected to a spring of stiffness k as shown An impulse is provided to the sphere at its mean position and the sphere starts oscillating Find the period of oscillation if there is no slipping anywhere 02360 k O mo

A block of mass m is attached with a spring in its natural length of spring constant k The other end A of spring is moved with a constant acceleration a away from the block as shown in the figure Find the maximum extension in the spring Assume that initially block and spring is at rest w r t ground frame A ma k 2ma B D 1 ma 2 k 4ma m wwwwwww A

A block of mass M is attached with a spring of spring constant K The whole system is placed on a vehicle as shown in the figure If the vehicle starts moving towards right with an acceleration a there is no friction anywhere then A Maximum elongation in the spring is 2Ma K 2Ma K B Maximum compression in the spring is Ma C Maximum elongation in the spring is K 2 Maximum compression in the spring is Ma 77 M a ooooo

10 A ball is rolling without slipping in a spherical shallow bowl radius R as shown in the figure and is executing simple harmonic motion If the radius of the ball is doubled the period of oscillation KVPY 20137 a Increases slightly b Is reduced by a factor of 1 2 c Is increased by a factor of 2 10

22 A parabolic bowl with its bottom at origin has the shape y x 20 Here x and y are in metres The maximum height at which a small mass m can be placed on the bowl without slipping coefficient of static friction is 0 5 is a 2 5 m ty vertical V b 1 25 m x horizontal c 1 0 m d 4 0 m

38 For a simple pendulum of length 0 7 m carrying a bob of mass 10 g and vibrating with an amplitude of 6 cm what is the PE at the extreme end of the string 2 52 x 104J 9 A simple pendulum is suspended from an inaccessible point It has a period of 4 s When the length is shortened by 119

38 A body is executing SHM At a displacement x its potential energy is E and at a displacement y its potential energy is E Find its potential energy E at displacement x y 1 E 3 E E E 2 E 4 E E E

4 A simple pendulum oscillates the amplitude oscillation is reduced to one third of its initia amplitude A at the ends of 10 oscillations Afte complete 20 oscillations its amplitude must be 1 3 20 20 2 4 Ao 4 2A 3

Questions 32 34 System A System B heeeeee Leeeee Systems A and B contain identical ideal springs and identical blocks that can slide along a surface of negligible friction In system A the surface is horizontal In system B the surface makes an angle with the horizontal Initially both blocks are at rest and in equilibrium Each block is then pulled the same distance d in the direction shown in the figures and released from rest at t 0 Hy 0 33 For system A when the block is halfway between its release position and its equilibrium position the block s kinetic energy is K and the elastic potential energy of the spring block system is U The ratio K U is A 1 3 B 1 2 C 1 1 D 2 1 E 3 1 34 A student wants to use an apparatus similar to system B to measure the acceleration due to gravity g If the mass of the block the force constant of the spring and the angle of the incline are known what additional data must be

A particle is performing simple harmonic motion giver by the equation y Asin wt If mass of the particle is m then average kinetic energy of the particle over a time interval of one time period is NI mw A 1 mm A 1mw A 8

With help of displacement x velocity v equation X v 25 100 For SHM determine time period 1 3 14 sec 3 6 28 sec 7 1 2 1 07 sec 4 4 21 sec 35

Two masses m m are suspended together by a massless spring of constant k when the masses are in equilibrium m is removed without disturbing the system the amplitude of vibration is Fe m m 1 3 mig k m m g k Audio ai foxx ZWHH U H v if f r Uf M H GU FA I GI 2 4 m2g k m m g k oooooor EE

A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad s The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad s and an amplitude of 102 m The relative change in the angular frequency of the pendulum is best given by 1 10 rad s 3 10 5 rad s 1 2 1 rad s 4 10 3 rad s

47 A second harmonic has to be generated in a string of length stretched between two rigid supports The points where the string has to be plucked and touched are respectively 1 4 2 3 2 2 2 4 1 3 1 IN 4 4 1 31 24

2 Two waves have equations x a sin wt and x a sin wt o If in the resultant wave the X2 frequency and amplitude remain equal to amplitude of superimposing waves the phase difference between them is 1 BIO M 2 2 3 TC 4 T