Simple harmonic motion Questions and Answers

L A block of mass M is tied to a spring of force constant k and placed on a smooth horizontal surface The natural length of the spring is L P is a point on the spring at a distance from its fixed end The block is set in oscillations with amplitude A Find the maximum speed of point P on the spring 4 atau yang g k M

A body is made of two rods AB and CD rigidly joined together to form a T shape Two springs are attached to this body and the body is free to rotate in a vertical pla about a horizontal axis passing through C as shown in the figure Then the angular frequency in rad s of small oscillation of this system is Mass of each rod is 5 m 6 kg and their lengths are L m Spring constant for each spring is K 96 N m 52 helle K C helle

An object of mass 0 2kg executes simple harmonic motion along the x axis with a frequency of 25 Hz At the position x 0 04m the object has a kinetic energy of 0 5J and potential energy of 0 4J The amplitude of oscillation is 1 0 05m 2 0 06m 3 0 01m 4 none of these

If the length of second s hand in a clock is 4 cm the angular velocity and linear velocity of the tip is T 1 rad s 1 30 1 2 3 6 15 T rad s 1 T rad s C 750 TC 1500 T 375 T m s m s m s

If two S H M of same frequency and amplitude are super mposed in same phase on the particle of mass m The motion of the particle will be 1 SHM 2 Oscillatory but not periodic 3 Periodic but not oscillatory

3 cm s 9 A ring of radius R is hung by a hail on its periphery such that it can freely rotate in its vertical plane The time period of ring for small oscillation is 1 T 2n 3 T 2T R g 2R g 2 T T R g 3R 5g 4 T 2

Two mutually perpendicular simple harmonic vibration of same frequency superimpose on each other The amplitude of two vibration is different and T they are differing each other in phase by resultant of superposition is 1 Parabola 2 Straight line 3 Elliptical A Circular The

Sir but answer is given as first how as you are stating its answer third 4 0 4 second Which one of the following graphs represents correctly the given wave equation at origin K 2 3 1 0 0 2 1S id tak m 2 3 N F 2 3 0 0 3 2 3 133 2 3 3 3 0 0 2 3 2 3 una y 2 3 sin 2rx 3mt 3 0 0 2 3 t N

3 Infinite 4 Maximum but not infinite A displacement equation of a particle executes S H M is x sin oot then a Mean position x 0 1 b Mean position x 2 c Time period 3 1 a d 0 d Time period 2 b c 2 0 3 a c 4 b d 14 4 37 x sin a x b c 371 d 37 1 a

A particle oscillating under a force F KX bv is K and b are constants then oscillator is 1 Simple harmonic oscillator 2 Linear oscillator 3 Damped oscillator 4 Forced oscillator

executing S H M is shown in fig given below Choose the correct statements vs time curve for a particle 15 displacement Ay 1 Phase of the oscillation is same at t Os and t 2s time s 2 Phase of the oscillation is same at t 2s and t 6s 711 3 Phase of the oscillation is same at t Is and t 7s 4 Phase of the oscillation is same at t Is and t 3 s 1 a d feeigen displacement 2 b c 3 pa 1 t 0s 2 t 2st 2 t 0 72t 2s 3 t 1s 72 t 79 4 t 1s 72 t 3

4 Four pendulum A B C and D are suspended from the same elastic support as shown in figure A and C are of same length while B is smaller than A and D is larger than A If A is given a transverse displacement C B A D 1 D will vibrate with maximum amplitude 2 C will vibrate with maximum amplitude 3 B will vibrate with maximum amplitude 4 All the four will oscillate with equal amplitude accillating under a force 5 f FAR a 1 2 3 4 U

Which one is the displacement function for wave Where S is the longitudinal displacement 1 S x t a sin ot ky 2 S x t a sin oot kx 4 3 S y t a sin cot kx 4 of a medium particle

A pipe 30 cm long is open at both ends harmonic mode of the pipe resonates a 1 source will resonance with the same sou observed if one end of the pipe is clos Take the speed of sound in air as 330 1 4th Harmonic yes 2 II Harmonic yes 3 4th Harmonic No 4 II Harmonic No

T Two perpendicular harmonic oscillations x a sin oot 2 y a sin at are superposed What will be the resultant motion y sin at T add af x asin at and

A particle moves under simple harmonic motion SHM in a straight line In the first s after starting from rest it travels a distance of a and in next T S it travels a distance of 2a in the same direction Then A B C D the amplitude of its motion is 4a the time period of its oscillation is 67 the amplitude of its motion is 3a the time period of its oscillation is 87

Q 15 An object undergoes simple harmonic motion Its amplitude is xo The speed of the object is v when its displacement Is xo 3 What is the speed when its displacement is so A V 3 C 3 2 v B 2 v D O

Sop Boud oss doo h 500 of 50 borge wood and 5 a 50 50 60 bed so b ordu oro 5 aus 5035 50000 Options b 2a b 2 3 2a 3a b 3a 2a b 36 2 h

Time period of a particle executing SHM is 8 sec At t 0 it is at the mean position The ratio of the distance covered by the particle in the 1st second to the 2nd second is Type Nu perical T

4 The phase difference between the two given waves is Y a sin ot 2 1 2 Y a cos ot 3 0 2 2 a X 2 x 4 2 4 Q 23 CST 6 PN Junction Diode TU 2

A uniform rod of mass M and length L is hinged a one end and a spring of stiffness constant 2K attached with rod as shown in the figure The arrangement is on a smooth horizontal surface Calculate the time period of oscillation for a small angular displacement M 1 2 27K mmmm 2K 2 2 M 6K

A uniform rod of length L and mass M is pivoted at the centre Its two ends are attached to two springs of equal spring constants k The springs are fixed to rigid supports as shown in the figure and the rod is free to oscillate in the horizontal plane The rod is gently pushed through a small angle 0 in one direction and released The frequency of oscillation is a c 1 12k 2TM 1 6k b d k 2TM 24k

Q9 A block of mass mis connected to two springs of force constants k and k as shown in figure The block moves on a frictionless table after it is displaced from equilibrium and releas The block exhibits simple harmonic motion with period A O B O C T 2n T 2n D T 2n m 772 k kq T 2n m k k kykz 2m 3 k k kyky m k k

Initially spring is compressed by 0 5 m and surface is smooth Choose the correct option s Initial potential energy in spring is 12 5 J Kinetic energy of block A when spring is at natural length for first time is 12 5 J Work done by all forces on B is zero till spring attains it s natural length for first time None of these A B 100 N m 2kg 000000000000 2kg

Two thin films of same liquid of surface tension T are formed between a smooth rectangular wire frame and two thin uniform straight wires each of mass m and length I connected to a massless non deformed spring of stiffness k and then the system is released from rest The maximum elongation produced in the spring is A C 2T K 6T K B D 4T K 8T K m l A B mmm D

A uniform circular disc of mass m and radius R is placed on a rough horizontal surface and connected to the two ideal non deformed springs of stiffness k and 2k at the centre C and point A as shown The centre of the disc is slightly displaced horizontally from equilibrium position and then released then the time period of small oscillation of the disc is there is no slipping between the disc and the surface A 2 C 2 5m 7k 5m 11k B 2 D 2 3m 7k 3m 11k m R R 2 ooooooo C 2K 0000000 qu rough

9 A mass is released from a height h and its time of fall t is recorded in terms of time period T of a simple pendulum On the surface of earth it is found that t 2T The entire set up is taken on the surface of another planet whose mass is half of earth and radius the same Same experiment is repeated and corresponding times are noted as t and T

Figure shows a container having liquid of variable density The density of liquid varies as p Po 4 3h Here ho and p are ho constants and his measured from bottom of the container A solid block of small dimensions whose density is Po and mass m is released from bottom of the tank fakaf aa chi za wzu fy gy qa s cefa P Po 4 3 3h ho qkaffa sta 31 us ho au po Audig ay h a fuga y dla ch much do I GA ho A The block moves to top and remains at rest at the top 2 fa ga am eff qz faz haze zga B The block will execute SHM T ofa z Correct Answer C D ho The block will be in equilibrium at h 2 e am ho 2 Correct Answer h Time period of the motion of the block 5ho 6g T 27

The position of vector of a particle that is moving in three dimensions is given by 7 1 2 cos 2cot i 3sin wt 31 k in an inertial frame All units are in Sl Choose the correct statement s The particle executes SHM in the ground frame about the mean position 1 2 3 The particle executes SHM in a frame moving along the ve z axis with a velocity of 3 m s The amplitude of the SHM of the particle when seen from appropriate reference frame is m The direction of the SHM of the particle when seen from appropriate reference frame is given by the vector

49 A simple pendulum oscillator has an amplitude A and time period T The time required by it to trave from x A to x 1 A 2 dan m gu vra vilas e Adx x 2 T 6 is 2 T 4 3 T 3 4 T 2

slipping C is the centre of disc and m 3kg k 10 N m The time period of small oscillations is L C sooooor 111 O 0 6 k 100000

A block of mass m is suspended separately by two cifferent springs and is having time periods T and T2 respectively If same mass is connected to series combination of both springs then its time period is 2 T T2 4 T2 T 1 T T T T 2 T T 34

Three travelling waves in same direction are superimposed The equations of wave are y Ao sin kx wt y 3 2A sin kx cot and y3 4A cos kx wt If 0 2 and the phase difference between resultant wave and first wave is 4 then is

A particle executes SHM with amplitude A and time period T At the time t 0 the particle is at its mean position then at what times the particle will have potential energy 50 and 75 of its total energy within t 0 to t T

Two blocks of mass m and 2m are connected to a spring and wrapped around a smooth pulley as shown in the figure Blocks are released together with spring in natural length Calculate the maximum elongation in meters of the spring Given 3 meter mg K m K 201

39 A 100 Hz sinusoidal wave is travelling in the positive x direction along a string with a linear mass density of 3 5 x 10 3 kgm 1 and a tension of 35 N At time t 0 the point x 0 has zero displacement and the slope of the string is n 20 Then select the wrong alternative a Velocity of wave is 100 m s b Angular velocity is 200m rad s c Amplitude of wave is 0 025 m d None of the above

2 A bob is suspended by means of a light string of length from a rigid support When the bob is in equilibrium it is given a horizontal velocity of 2ge then 1 it moves in vertical circle 2 it oscillates 3 tension is not zero at any point 4 velocity is not zero at any point

Q 2 Two pendulums each of length 1 are initially situated as shown in figure The first pendulum is released and strikes the second Assume that the collision is completely inelastic and neglect the mass of the string and any frictional effects How high does the centre of mass rise after the collision The 7 d 1 Ma

A particle executing simple harmonic oscillation has an amplitude 14cm and time period 1 6sec Calculate the time taken by the particle to travel a distance 7 5cm away from the mean position Ans 0 161 sec

the velocity of the sound wave Ans 120 96m sec The velocity of a particle executing simple harmonic oscillation is 1 4m sec and 0 8m sec when it is 22cm and 48cm away from the mean position Find its time period and amplitude Ans 2 331sec 56 44cm Calculate the fraction of kinetic energy and potential energy to the total energy when the tin

is 22cm and 48cm away from the mean position Find its time period and amplitude Ans 2 331sec 56 44cm Calculate the fraction of kinetic energy and potential energy to the total energy when the displacement of the particle executing simple harmonic oscillation is 1 3 of its amplitude Ans E E 8 9 E E 1 9

Find the angular frequency of SHM of block of mass m for small oscillation of light rod BD Consider rod is vertical and springs relaxed in initial state RE k k c mikic k b c k D 6000000 m moo k 6000000 1 600 B Figure 5 88

5 37 A hollow sphere of radius r is rotating about a horizontal axis at some angular speed oo It is gently lowered to ground and the coefficient of friction between sphere and the ground is How far does the sphere move before it starts pure rolling 2 2 2 wor Ans 5 25 119

al nt t SS m bob is 6 22 A simple pendulum is a device in suspended from a support by means of a string figure 6 108 If the string is pulled aside by a small angle from the vertical and released the bob executes simple harmonic motion For two pendula whose bob have the same gravitational mass at one of which has an inertial mass 1 larger than the other show that the one with the larger inertial mass has a time period approximately 0 5 greater than the other one 0 tagitany m

rictionless floor 1 A block of mass M 6 00 kg slides at a constant speed V on a frictionless floor towards a spring fixed to a wall The block gets attached to the free end of the spring on contact The spring gets compressed by X cm and then continues to perform simple harmonic vibrations Take displacement and motion to the right as positive and the initial position of the block on contact with the spring to be x 0 Setup A The speed V 5 00 m s and the spring is compressed by X 12 0 cm Setup B The maximum speed Vmax 10 0 m s and amplitude of vibration of the spring X 24 0 cm a What is the maximum speed of the block in setup A 1 5 00 m s 6 00 m s 12 00 m s 30 0 m s 24 0 m s

A uniform disc of mass m can roll without slipping C is the centre of disc and m 3kg k 10 N m The time period of small oscillations is A 0 6T C 0 9T k 1000001 k 100000 m B 0 3m D 0 1

simple harmonic motion is given by y A Asinot Bcoswt Then the amplitude of its oscillation is given by 2 1 Ao A B lo 2 A B ions 3 A2 A 4 A B s Limited

19 A particle is executing SHM according to equation 4 its displacement at t 2 s is 20 y 10 cos 2rt 10 2 2 m 1 5 2 m 3 5 m 4 Both 1 2 Five moles of hydrogen gas are heated from 30 C

A hollow cylindrical shell of radius R has mass M It is filled with water having mass m and placed on an inclined plane connected to a spring spring constant k as shown in the figure When it is disturbed it performs oscillations without slipping on the inclined plane a Find the time period of the resulting oscillation b If the water in the given case freezes into ice which is tightly pressed against the inner surface of the cylinder then find the time period of the resulting oscillation M m 0 www X

A point mass m is attached on massless rod of length L The rod is hinged frictionless hinge The hinge is constrained to oscillate vertically with harmonic motion h t h cost The only freedom is which measures the angle of rod from vertical Find 1 Lagrangian and 2 the equation of motion Hinge Pistons L h t Grav Y