Simple harmonic motion Questions and Answers

73 A particle is moving along x axis x in metre and force acting on particle varies as F 5x 5N then A 1 Motion of particle will be circular 2 Motion of particle will be periodic having mean position at x 1 m 3 Equilibrium position of particle will be at x 4m 4 Both 1 2

any instant is x then differential equation of S H M of the block can be given by ww 1 d x dt 3 k m k d x 2 dt 4m d x 2k dt m k X 0 X 0 X 0 000000000 KR a 27 hx mg

6 radius 3R is filled with a dielectric of dielectric constant K 3 an conductivity o Initial charge given to the capacitor is Qo Due to finite conductivity of the dielectric the charge leaks out with tim constant Calculate the value of x G 3R

1 3 3 53 A spring block system in horizontal oscillation has a time period T Now the spring is cut into four equal parts and the block is re connected with one of the parts The new time period of vertical oscillation will be m T 2 T 0 4 2m m 2 27 T 4 255 X is 1 3 59 If tw mots zera them 1 3

31 A spring has equilibrium elongation 0 1 m suspended vertically with a load If the load is slightly displaced vertically downward and released then time period of SHM of the system will be approximately 1 0 1 s 2 0 4 s 3 0 6 s 4 0 3 s

05 Instantaneous accel executing S H M is given by a sin 4 6 The maximum speed of the particle will occur first time at 1 1 75 s 3 12 s 2 1 4 s 4 0 67 s

35 If a Second s pendulum is moved to a planet where acceleration due to gravity is 4 times the length of the second s pendulum on the planet should be made 1 2 times 3 8 times 2 4 times 4 15 times

46 A solid cylinder of density Po cross section area A and length floats in a liquid of density p Po with its axis vertical as shown If it is slightly displaced downward and released the time period will be 1 2m b 3 2 121 2 2 pl Pog 2g Aakash Educational Services Pvt Ltd Regd Office Aakas pg 4 2m

212 The quality factor of a tuning fork of frequency 512 Hz is 6 10 Calculate the time in which its energy is reduced to e of its energy in the absence of damping How many oscillations will the tuning fork make in this time

The period of oscillation of a simple pendulum is 41 T 2 L g B di 1 20 0 cm 11 mm T 2 L g Measured value of L is 20 0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution What is the accuracy in the determination of g approx 1 1 2 9 3 6 4 3 44 a 100 490 Aufka nefan EFTFT 1 1 2 9 3 6 4 3

25 A disc of radius R and mass m is pivoted at its and is set to small oscillations If simple pendulum have same time period then effective length of pendulum is 1 R2 3 R 2 4 3R 2 1 0

17 A 2 70 kg mass is pushed against a horizontal spring of force constant 0 310 N m on a frictionless al table The spring is attached to the tabletop and the mass is not attached to the spring in any way When the spring has been compressed enough to store 15 0 J of potential energy in it the mass is suddenly released from rest Find a the greatest speed the mass reaches and b the greatest acceleration of the mass

Question No 3 A particle is moving in a uniform circular motion on a horizontal surface Particle s position and velocity at time t 0 are shown in the figure in the coordinate system Which of the indicated variable on the vertical axis isla correctly matched by the graph s shown alongside for particle s motion x component of velocity y component of force keeping particle moving in a circle t y vat t 0 X

Two particles are executing simple harmonic motion of the same amplitude A and frequency w along the x axis Their mean positions are separated by distance xo xo A If the maximum separation between them is co A the phase difference between their motions is A B C 13 Correct Answer 4 6 Your Answer

A particle executes linear simple harmonic motion with amplitude of 3cm When the particle is at 2cm from the mean position the magnitude of its velocity is equal to that of its acceleration Then its time period in seconds is 27 4T 5 2T 5 70 Phy Se Choose 1 01 5 9 13 17 21 25

Capacitor of capacitance C is connected to parallel conducting rails A conducting rod of mass m and length connected to spring of spring constant k is placed on rails The whole arrangement is placed in magnetic field of magnitude Bo which is perpendicular to plane If spring is initially compressed by xp it takes C 000000000 m B C time to get back to initial position Find a auk

The displacement of a particle executing SHM is 22 given by y 10 sin 6t 3 where y is in metre at time t in seconds The initial displacement and velocity of the particle are respectively 1 5 3 m and 30 m sec 2 15 m and 5 3 m sec 3 15 3 m and 30 m sec 20 3 2 m and 30 m sec una ma fa and go 44 45 y 10 sin 6t a 3 for farten z 2 1 5 3x3 30 2 15 2 3 5 3 3 15 323 30 4 20 3 2 30 s

A mass M is suspended from a spring of 24 negligible mass The spring is pulled a little and then released so that the mass executes SHM of time period T If the mass is increased by m the time period becomes 5T 3 The ratio of m M is 25 1 3 9 and fant fest at its fra forrets fem f r O 1 in len f en 5 3 2 3 16 4

A simple pendulum is suspended in a car The 30 KES ERG CICES ER car starts moving on a horizontal road according to equation x 3 2 oscillation of the pendulum 1 2n 3 2T 3 Find the time period of 8g 2 T 2n 20 g 8 3 OR ONLINE LEADER TEST SERIES JOINT PACKAGE COURSE S Page 8 36 1 2n 3 Residen 2n 8g Space for Rough Work ferg re 2 2 T 2n 20 8 3 0999 OMD61091968 NEET UG 2020 2107202

14 If the displacement of the particle at an instant is given by y r sin wt 0 where r is amplitude of oscillation co is the angular velocity and is the initial phase o e particle then find the particle velocity and particle acceleration Ans r o cos wt 0 1 W suiwel

3 0 14 m s Two simple harmonic motions are represented by the following equations x 4sin2nt and x 2 sin2rt cos2 f then ratio of their amplitude is 1 2 2 1 1 3 To 4 2

3 m s 4 28 m s A body is executing SHM with amplitude a and time period T The ratio of kinetic and potential energy when displacement from the equilibrium position is half the amplitude 1 1 1 2 2 1 3 1 3 4 3 1 long axis is given by U 5x x 4 where x

3 5 points A spring is stretched 5cm by a force of 1 N A mass of 1kg is hung from the spring and is also attached to a viscous damper that exerts a force of 2 N when the velocity of the mass is 3 m s The mass is pushed up 2 cm above its equilibrium position and given an initial downward velocity of 4 m s Set up a differential equation with initial value to describe the position of the weight at any time t

Q41 A mass m is undergoing SHM in the vertical di rection about the mean position yo with amplitude A and angular frequency w At a distance y from the mean position the mass detaches from the spring As sume that the spring contracts and does not obstruct the motion of m Find the distance y measured from the mean position such that the height h attained by the block is maximum Aw g 2005

Objective Typ A particle is undergoing SHM when its kin energy is equal to potential energy the velocity particle is w angular frequency A amplitu and potential energy at mean position is zero WA 1 2 16 M A 2 4 2wA

Q3 16 Mar 2021 Shift 2 mathongo mathongo mathongo matho A deviation of 2 is produced in the yellow ray when prism of crown and mathongo mathonge mathongomathongo mathongomatho flint glass are achromatically combined Taking dispersive powers of mathongo mathongo mathonge mathongo mathongo mathongo mathongo matho crown and flint glass are 0 02 and 0 03 respectively and refractive index matho mathongo mathongo mathongo mothongo mat haq for yellow light for these glasses are 1 5 and 1 6 respectively The mathonto mothongo pmathong thongo refracting angles for crown glass prism will be mathongo mathongo Round off to the Nearest Integer mathongo in degree matho mothongo matho

20 The time period of a given spring mass string system is 1 2 2 2 K oooooo Spring m 2K m K Block m K Elastic string

If the length of a stretched string is shortened by 40 and the tension is increased by 44 then the ratio of fina and initial fundamental frequencies is 02 1 3 2 3 4

6 The length of a simple pendulum is decreased by 21 Find the percentage change in its t period In procutes SHM on a straight line path The amplitude of oscillation is 2 cm When of magnitud

1 A particle is subjected to two simple harmonic motions of the same frequency and direction The amplitude of the first motion is 4 0 cm and that of the second is 3 0 cm Find the resultant amplitude if the phase difference between the two motions is a 0 b 60 c 90 d 180

Physics Question No 27 Question Palette Two particles undergo SHM along parallel lines with same time period of 8 s and equal amplitude of 2 cm At a particular instant one particle is at extreme position while other is at its mean position They move in the same direction From this moment they will cross each other after Options

A block is restricted to move in a smooth groove It is connected to a spring of spring constant K Neglecting the effect of gravity block is allowed to oscillate along the groove Time period of small oscillations of block will be 1 2 3 k m 2x LEI m m mass of block m 2 2x sine k 4 2 mcos

3 It will sink 4 Same part in water 17 The maximum force acting on body executin SHM is F and the maximum energy of the body i E Amplitude of the motion of the particle is 1 2 2F 2 4 F 2E

4 x B A sinot 20 A particle is executing S H M along x axis with origin as the mean position If velocity v of the particle is related with position x as 9v 36x then time period of the oscillation will be 1 3s 3 6s 2 3TS 4 6TS

18 A travelling wave pulse is given by 10 where symbols have their usual 2 x 3t meanings x y are in meter and t is in second then 1 The pulse is travelling along ve y axis 2 The pulse is travelling along ve y axis 3 The amplitude of wave pulse is 10 m 4 The velocity of wave pulse is 3 m s y

8 Two masses m and m are suspended together 4 by a massless spring of constant K When the masses are in equilibrium m is removed with disturbing the system The amplitude of oscillations is 2 mg m EE x A xetx m mc g K mg mes 2 4 mea

3 12 RTD In2 4 4 RT In2 31 A particle of mass 10 g is executing SHM according to the equation y 4 sin 4t 3 having time period T Kinetic energy of the particle at t T 4 will be 1 9 6 unit 2 0 48 unit 3 1 92 unit 4 0 96 unit 32 A uniform ladder of mass m 40 kg rests against

5 V Two blocks A and B are kept over a smooth horizontal surface as shown There is friction between blocks A and B Initially both blocks lie at x 0 with spring at its natural length Now block B is pushed towards left and then released Spring block system undergoes simple harmonic motion with amplitude A The block A tends to slip over B A is most likely to slip at A X 0x C x A 2 B x A D X A 2 Space for Rough world ooooooo A B Frictionless surface 0

Two blocks A and B are kept over a smooth horizontal surface as shown There is friction between blocks A and B Initially both blocks lie at x 0 with spring at its natural length Now block B is pushed towards left and then released Spring block system undergoes simple harmonic motion with amplitude A The block A tends to slip over B A is most likely to slip at A x 0 C x A 2 Spaco B x A D x A 2 ooooooo A f B Frictionless surface 0

A soap film is formed on a parabolic vertical rigid fixed frame y 4x A sufficient long thin rod is hanging with frame with support of film in uniform gravity as shown in diagram Now rod is slightly displaced in vertical direction and released T is surface tension Take complete wetting condition Mass of ro is m A AC B AD D BD X axis H BC Y axis A Initially equilibrium of rod is stable B Initially equilibrium of rod is unstable C For small oscillations time period of oscillation will be 2 m H 2T D For small oscillation time period of oscillation will be 2 m H T

3 8 5 A particle is executing SHM about y 0 along y axis Its position at an instant is given by y 7 m sin nt Its average velocity for a time interval 0 to 0 5 s is 1 14 m s 2 7 m s 1 3 m s 7 4 28 m s porind I The ratio of kinetic and potential energy when

5 For the travelling harmonic wave y x t 2 0 cos 2 10t 0 0080x 0 35 where x and y are in cm and t in second The phase difference between oscillatory motion of two points separated by a distance 4 m will be 1 9 4 rad 3 6 4 rad 2 2 4 rad 4 7 4 rad

4 Figure shows the velocity executing SHM The correct equation for displacement time x t representing this motion NCERT Pg 345 v cm s is 10T 0 10T 1 x 50 cos LO 5 Ft 5 Ft TC 2 x 50 sin t cm 5 3 x 10 sin t cm sint 5 10 o cm 15 t s

Online Mock Test Series for NEET 2 2 A particle performing SHM with freque 10 Hz and amplitude 5 cm is initially in extreme position The equation of displacement will be x is in metre 1 x 0 05 sin 20nt 2 2 x 0 05sin 20xt 3n 2

A simple pendulum of length 1m is allowed to oscillate with amplitude 2 It collides elastically with a wall inclined at 1 to the vertical Its time period will be use g Question Type Single Correct Type 1 2 3 2 3 sec 4 3 sec 2 sec

4a 2a The amplitude of vibration of particle is given by a am where a a b and care am bo c positive The condition for single resonant frequency will be 1 b 4ac 3 b 4ac 2 b 4ab 4 Both 2 and 3 des X X 1 3

3 R 12 A particle starts oscillating simple harmonically from its equilibrium position Then ratio of kinetic T energy and potential energy of particle at is 1 2 1 3 1 1 2 3 1 4 1 4

In the arrangement shown in the figure a heavy pulley of mass M is suspended from a spring of stiffness constant K and the mass m is suspended from a string tightly wound on the pulley If the mass m is given a small downward displacement and released find the time period of small oscillations Take pulley as Disc and string does not slips on the pulley M elle

Q 1 A spring with mass 2 5kg has a neutral length is 0 6 m It immersed with a fluid wit damping modulus equal to 50 Find the position of mass at any time t if starts from equilibrium position with initial velocity V 0 8 m sec Take K 130 N m

3 kg sphere dropped through air has a terminal speed of 25 m s Assume that the drag force is bv Now suppose the sphere is attached to a spring of force constant k 300N m and that it oscillates with an initial amplitude of 20 cm What is the angular frequency of its damped SHM B 9 998 rad s D 10 01 rad s A 9 996 rad s C 10 00 rad s