Simple harmonic motion Questions and Answers

The potential energy of a particle of mass m executing SHM along the x axis is given by U Uo Uo cosax The time period of small oscillation of the particle is 2 U a m m 02 17 a U 2 m 03000 3a Uo 3 Uo

4 Two pendulums of time periods 3 S respectively start oscillating simultaneously from two opposite extreme positions After how much time they will be in same phase 21 21 a S 8 b S 4 21 c s IS 2 Pisv d 21 10 S se buc tion of a SHM has a period

5 A particle of mass 1 g executes an oscillatory motion on the concave surface of a spherical dish of radius 2 m placed on a horizontal plane If the motion of the particle begins from a point on the dish at a height of 1 cm from the horizontal plane and the coefficient of friction is 0 01 the total distance covered by the particle before it comes to rest is approximately x meter Find value of x

In the arrangement shown in the figure a pulley of mass M is suspended from a light spring of stiffness constant k and a mass m is suspended form a string tightly wound on the pulley If the mass m is given a small downward displacement and released the time period of its small oscillations is Assume that the string does not slip on pulley 8m 3M 2k B 27 3m 8M 2k M leee C 2 3M 8m 8M 3m D 27 k

A simple harmonic oscillator of angular frequency 2 rad s is acted upon by an external force F sint N If the oscillator is at rest in its equilibrium position at t 0 its position at later times is proportional to 2015 1 1 sint cos 2t 2 3 sint sin2t 2 17 12 2 cost sin 2t 1 4 sint sin 2t 2

In the figure two tiny conducting balls of identical mass m and identical charge q hang from nonconducting threads of length L Assume that is so small that tan 0 can be replaced by its approximate equal sin 8 If L 130 cm m 10 g and x 3 9 cm what is the magnitude of q L ee 1

A particle describes SHM in a straight line about O P 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 1 T 2 2 1 3 T 2 2

7 A particle of mass 0 1 kg is executing SHM of amplitude 0 1 m When the particle passes through the mean position its K E is 8 x 10 J Find the equation of motion of the particle if the initial phase of oscillation is 45 TC 1 y 0 1cos 3t 4 TU 3 y 0 1sin 4t 4 2 y 0 1sin 6t TU 4 4 y 0 1cos 4t 4

View In English 27 solid cone made of a material of relative density S and height H 4m floats with its apex downward in water The time period of vertical oscillation if it is slightly displaced from the 64 uilibrium position is T find value of T Assume n q 1 15 Pw H

2 If the total mechanical energy of the system is 73 5 Joules what are the amplitude maximum speed and maximum acceleration of the motion The amplitude A Units Select an answer The maximum speed Vmax The maximum acceleration amax Units Select an answer Units Select an answer

1 A 4 5 kg mass is attached to an ideal 650 N m spring If the system undergoes simple harmonic motion what are the frequency angular frequency and period of the motion The frequency f Units Select an answer The angular frequency w The period T Units Select an answer Units Select an answer C

The equation of motion is represented by y sin oot cos ot The time period of periodic motion is NCERT Pg 339 1 3 F3 2 2 4 2 4 The equation of motion of particle executing 1 o VENTA ot promet 21 vorene XA 2 0 16 au XA

ose time e will be Pg 351 one 50 ch of S CAMERA 12 A spring having spring constant of 800 Nm 1 is mounted on a horizontal table as shown A mass of 2 kg is attached to free end of the spring The mass is pulled sideways to distance of 2 5 cm and released How much time the mass takes from one extreme to other NCERT Pg 359 6 1 0 157 s 3 0 314 s ANNA K voorr m Fixed 2 0 2 s 4 0 782 15 A spring balance has a s 0 to 100 kg The length Maps A block suspended from bollar of man displaced and released spring com period of 0 2 s What approximately placed fr stance of equency 1 2 kg 2 4 kg 3 5 kg 4 6 kg 16 The graph between length 1 5 4 2 13

15 A spring balance has a scale that reads from 0 to 100 kg The length of scale is 25 cm A block suspended from this balance when displaced and released oscillates with time period of 0 2 s What is mass of block NCERT Pg 359 approximately 1 2 kg 2 4 kg 3 5 kg 4 6 kg DUAL CAMERA 16 The graph between length of pendulum and Nm 1 nown of the s to uch e to 59 A 17 to a sp of spring constant 500 Nm 1 If coll displaced from equilibrium position distance of 2 cm and released w frequency of oscillation 1 5 4 Hz 2 1 78 Hz Collar NCERT P m 4 kg 2021 07 29 21 32

5 A plane electromagnetic wave propagating in the x direction has wavelength of 6 0 mm The electric field is in the y direction and its maximum magnitude of 33 V m The equation for the electric field as function of x and t is a 11 sinn t c 33 sinn t C b 33 sinn 10 t x C d 11 sin x 10 t X

is balance s 25 scillates with s mass of b NCERT Pg 3 benduluma shown bel RAT PO 17 A collar of mass 4 kg is attached to a spring of spring constant 500 Nm If collar is displaced from equilibrium position by a distance of 2 cm and released what is frequency of oscillation p 1 5 4 Hz 2 1 78 Hz 3 9 36 Hz 4 3 26 Hz Collar NCERT Pg 348 m 4 kg 1 2 3 T 2 T 3 2T 4 V3 xT 19 A particle executes S energy which change potential energy at ec assumed to be zero

The equation of motion of particle executing SHM is given as y sin ot The position of equilibrium is NCERT Pg 341 1 y 0 3 y 1 2 2 y 1 4 y 1 A body execute SHM according to equation

O A pendulum is made of a rigid rod mass m length I and a small bob of mass M attached at one end as shown in the figure The rod is pivoted on the other end What should be the minimum speed of the bob at its lowest point so that the pendulum completes a full circle A 12M 6m V 3M m gl B 4gl C 5gl D 15M 6m gl 3M m m M

7 The period of oscillation of a simple pendulum of length L suspended from the roof of a rocket accelerating upwards with a constant acceleration g is given by A 00 B 0 C 2A D 2

78 Period of small oscillations in the two cases shown in figure is T and T2 respectively Assume fluid does not have any viscosity then a T T c T T wwwwwww m eeeeeeee k m k b T T d Cannot say anything

sir the theory that has given in package of aakash accordi ng to this the answer of this question should be option 2 b ut it is given option 1 in package why what is the differen ce between these two concepts VP 7 A loaded vertical spring executes S H M with a time period of 4 s The difference between the kinetic energy and potential energy of this system varies with a period of 1 2 s 3 8 s 8 As a body performs SHM its potential enerav U V III 2 1 s 4 4 s EU X K U A IK U 0 O 778 O 714 772 3714 T 3 From the figure given below it is clear that IK U completes its one cycle maximum to zero anc zero to maximum in time so its frequency is four times the frequency of SHM x A E U80 K MU 718 K U M 1 K 40 E FOR a A

65 The vertical motion of a ship at sea is described 4x where x is the vertical c 0 2 d x the equation dt2 height of the ship in metre above its mean po If it oscillates through a height of 1 m a its maximum vertical speed will be 1 ms1 b its maximum vertical speed will be 2 ms c its greatest vertical acceleration is 2 ms 2 d its greatest vertical acceleration is 1 ms 2

29 Figure shows the circular motion of a particle The radius of the circle the period sense of revolution and the initial position are indicated in the figure The simple harmonic motion of the x projection of the radius vector of the rotating particle P is T a x 2 cos 2 t 4 13 2 cm 0 45 P t 0 T 1 s perg T b x 2 sin 2 t 4

a 1 cm b 2 cm c 3 cm 8 14 3 Simple Harmonic Motion Out of the following functions representing motion of a particle which represents SHM 1 x sin wt 2 x 1 t 0 3 x coswt cos3wt cos5 t 4 x sinot cos t a Only 1 c Only 1 and 4 d 4 cm b Only 1 and 3 d Only 4 c The function sinc a a simple harm 9 Which of the following is not a characteristics of simple harmonic motion a The motion is periodic b The motion is along a straight line about the b a simple harm c a periodic b with a period d a periodic b with a period A particle exec

Out of the following functions representing moti of a particle which represents SHM 1 x x sin 0t 2 3 x cos t cos3wt cos5wt 4 x sinoot cos t a Only 1 c Only 1 and 4 on x 1 wt w R b Only 1 and 3 d Only 4

66 A simple pendulum is suspended from the ceiling of a car and its period of oscillation is T when the at rest The car starts moving on a horizontal road with a constant acceleration g equal to the acceleration due to gravity in magnitude in the forward direction To keep the time period same the length of the pendulum 2 a will have to be increased by 1 b will have to be increased by 2 1 1 c will have to be decreased by 21 d will have to be decreased by 2 1 slonia

A particle of mass m is in a one dimensional potential field and its potential energy is given by the following equation U x U 1 cos ax where U and a are constants The period of the particle for small oscillations near the equilibrium will be 1 2n 2 ma ma U m 2 2 ma U a U 28 H

A particle of mass m undergoes oscillations about x 0 1 in a potential given by V x 10x V cos 2 where 2 Vak a are constants If the amplitude of oscillation is much smaller than a the time period is given by m V B 27 C 2 ma 2 ka Vu D 2 ma FPECE J2 V

A spring oxocutos SHM with mass of 4 kg attached to it The force constant of spring is 100 N m If at any instant its velocity is 40 cm s the displacement from the mean position will be Here amplitude is 0 5 m 1 006 m 2 03m 3 0 49 m 4 10m

A particle perform simple harmonic motion with amplitude A and time period T Average speed of the particle over the time interval during which it travels a distance of starting from extreme position is 4A T 3A T O3A 27 37

wo blocks of masses m and 2m are connected to a massless spring of force constant k The spring is stretched by x and the blocks are made to oscillate on a mooth horizontal surface The amplitude of motion of block of mass m is O xo 3 2x0 3 O xo m k 000000 2m

d All of the above r 6 A particle of mass 2 kg moves in simple harmon emotion and its potential energy U varies with position x as shown The period of oscillation of the particle is 13 ing sin Periodic w t a c 2 5 2 T S R S U 1 O 0 4 2 2 5 b x m d 4t 5 S S

54 The equation of motion of a particle is x a cos a t 2 The motion is a periodic but not oscillatory b periodic and oscillatory c oscillatory but not periodic d Neither periodic nor oscillatory NCERT Exemplar is attached to the lower end of a 10 Nm the 1 9

A block of mass m is kept on smooth horizontal surface and connected with two springs as shown in figure Initially springs are in their natural length Time period of small horizontal oscillation of the block is m kg k 22N m 00000000 4k 30 m 007

A block of mass m is kept on smooth horizonal surface and connected with two springs as shown in figure Initially springs are in their natural length Time period of small 7 horizontal oscillation of the block is m m 2 2kg k 22N m 4k 100000000 30 100 m000000

A spring block system is placed on smooth horizontal surface as shown Initially spring is in natural length o Maximum expansion in cm in spring in subsequent motion is k 100N m 1kg 6000000000000 2kg 20N

33 For a simple harmonic oscillator A potential energy varies linearly with displacement from equilibrium B spacing between energy levels increases with increasing energy C spacing between energy levels decreases with increasing energy D number of nodes of the wave function increases with increase in energy

simple harmonic with amplitude 32 In case of a simple pendulum time period versus length is depicted by a T c T 1 d T 2 1 Ta Je 2 of particle is

Please explain how to tackle this type of questions A solid ball of mass M and radius R is rolling without slipping on a flat horizontal surface at an initial angular velocity wo It hits a small bump of height h Assume that the ball pivots about the tip of the bump during and after impact Which of the following statements are TRUE R The angular velocity of the ball immediately 5h 1 5 PR after impact is ol The minimum initial angular velocity so that the ball just makes it over the bump is 7 10gh

The potential energy of a particle of mass mexecuting SHM along the x axis is given by U Up Up cosax The time period of small oscillation of the particle is O O a m 2x L ES

Two simple harmonic motions are represented by equation y 3 sin 10 t and Y 5 cos 10 t Determine phase difference between their velocities 2

The position vector of a particle that is moving in three dimensions is given by F 1 2 cos 2wt i 3 sin wt j 3t k in the ground frame All units are in Sl Choose the correct statement s 3t T The particle executes SHM in the ground frame about the mean position 1 B The particle executes SHM in a frame moving along the z axis with a velocity of 3 m s 5 The amplitude of the SHM of the particle is m 2 The direction of the SHM of the particle is given by the vector Doy 15 35 3

A box of mass 14m with smooth base is sliding on an inclined plane of inclination 0 under the influence of a force F A string of mass m length is attached at A The box is released from rest and a transverse pulse is produced at other end B Mark the correct statement s for the pulse A if F 0 the pulse will remain stationary B if F 0 the pulse will not reach to end A FA 37 5 C For F 9 mg the time taken by the pulse in moving from B to A will be 2 3g 50 D if F 18 mg the time taken by the pulse in moving from B to A will be 2 3g

16 In order that the resultant path on superimposing two mutually perpendicular SHM be a circle the conditions are that a the amplitudes on both SHM should be equal and they TC should have a phase difference of 2 b the amplitudes should be in the ratio 1 2 and the phase difference should be zero c the amplitudes should be in the ratio 1 2 and the TU phase difference should be 2 J 1

A metallic ring connected to a rod oscillates freely like a pendulum If now a magnetic field is applied in the horizontal direction so that the pendulum now swings through the field the pendulum will 1 Keep oscillating with the old time period 2 Keep oscillating with a smaller time period 3 Keep oscillating with a larger time period

The length of a magnet is large compared to its width and breadth The time period of its oscillation in a vibration magnetometer is 2 s The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together The time period of this CII

A simple pendulum of effective length is hanging from a ceiling of a trolley which is coming down an inclined plane of an angle 0 with a constant velocity The time period of simple pendulum is given by 1 2 3 2 1 g cose 1 2 2 4 2 1 g sin e

A simple pendulum performs simple harmonic motion abou x 0 with an amplitude A and time period T The speed of A the pendulum at x will be 3 C TA 2T 3 A4 3T 1 L 100 T TA 18

An air chamber of volume V has a neck area of cross section a into which a ball of mass m just fits and can move up and down without any friction Fig 14 27 Show that when the ball is pressed down a little and released it executes SHM Obtain an expression for the time period of oscillations assuming pressure volume variations of air to be isothermal see Fig 14 27 m a

Assorted qu Which of the following quantities is always negative in SHM b v s c a s d F v a F a Here s is displacement from mean position endulum the period of oscillation T dulum las