Simple harmonic motion Questions and Answers

All India Major Test Series Phase I II Major Test 28 22 03 06 2020 Asin t kx NEET PHYSICS Q 97 A transverse wave is described by the Q 97 equations Y Asin t kx The maximum particle velocity is equal to the wave velocity if the value of A is 1 3 k 3 1 k 2 2 k 4 None of these 1 3 k 3 1 k f 2 2 k 4

b A 50 g mass vibrates in SHM at the end of a spring The amplitude of the motion is 20 cm and the period is 0 02 s Find i the frequency of vibration ii the value of the spring constant and iii the maximum speed of the mass

The displacement d in meters of an object at time t in seconds is given by the following equa d 3 cos OD No because the given equation is not in the form of d a sin t b What is the maximum displacement from its resting position meters c What is the time required for one oscillation second s Simplify your answer Type an exact answer using it as needed Use integers or fractions for any m d What is the frequency oscillation per second Simplif

A simple pendulum is suspended from the ceiling of a car accelerating uniformly on a horizontal road with acceleration 9 If length of pendulum is then time period of small g 2 oscillations about mean position is 2 2T 20 5g O 2T 20 5g 2

The momentum v s displacement from mean position graph of a particle of mass 2 kg performing simple harmonic motion is given by P kg m s 8T 2 x m A Time period of particle is 1 s B Maximum acceleration of particle is 8 m s C The velocity of particle is 2 m s when it is at distance 3m for mean position D Maximum kinetic energy of particle is 167 joule

5 A rectangular block of mass m and area of cross section A floats in a liquid of density If it is C given a small vertical displacement from equilibrium it undergoes oscillation with a time period T Then AIPMT Prelims 2006 1 T p 2 Tx 1

A body of mass 2025 kg moves in simple harmonic motion making 90 double strokes per minute each 390 mm long If the acceleration at the end of the stroke is 17 3 m s Calculate 2 1 The maximum velocity and maximum kinetic energy of the mass 2 2 The velocity and acceleration at one third stroke 5 8 421

10 The displacement y in cm produced by a simple harmonic wave is y 7 periodic time and maximum velocity of the particles in the medium will respectively be A 10 sec and 330 m sec C 10 sec anc 20 m sec B 10 sec and 20 m sec D 10 2sec and 200 m sec sin 200

ALLEI 21 Four pendulums A B C and D are suspended 21 from the same elastic support as shown in figure A and C are of the same length while B is smaller than A and D is larger than A if A is given a transverse displacement 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 Speed of sound waves in a fluid depends upon 22

A mass of 0 5 kg is attached to the end of a spring To stretch the spring 2 m in the positive x direction beyond its equilibrium position a force of 36 N must be applied The mass is then pulled x 0 0 3 m from equilibrium position and set in motion with an initial velocity of 6 m s Find the position x t of the mass at any time t

In the case of forced oscillation which of the Following statements is not true Frequency equals that of external periodic force Amplitude depends upon the damping coefficient Amplitude tends to infinity at resonance Higher the damping coefficient lower is the amplitude at resonance

mass of 0 5 kg is attached to the end of a spring To stretch the spring 2 m in the positive x direction beyond its equilibrium position a force of 36 N must be applied The mass is then pulled x 0 0 3 m from equilibrium position and set in motion with an initial ocity of 6 m s Find the position x t of the mass at any time t

2 A mg B Mg A block of mass m is pressed against a vertical surface by a spring of unstretched length l If the coefficient of friction between the block and the surface is Choose the correct statement 2mg A If spring constant k d moooooooo B If spring constant is k block will not be in equilibrium 2mg d C In the part B force of friction is 2mg D Minimum spring constant kmin to keep the block mass M is equilibrium is mg the normal reaction is mg ud shome

A simple pendulum attached to the celling of a stationary lift has time period T The lift starts moving and the position vector of the lift is given as r t 15t i 15t23 where r t is in meters and t is in seconds If g 10m s2 the new time period of oscillation is

Two simple pendulums of length 1 m and 4m respectively are both given small displacement in the same direction at the same instant They will be again in phase after the shorter pendulum has completed number of oscillations equal to 2013 12 3 5 2 7 4 3

plz solve it within 30 40 mins I ll give you multiple upvote A 4 kg mass is attached to a spring hanging from the ceiling thereby causing the spring to stretch 3 92 m upon coming to rest at equilibrium At time t 0 an external force of F t 3 cos t N is applied to the system The damping constant for the system is 8 N sec m Determine the steady state solution for the system The stiffness of the spring is k Type an integer or a decimal The steady state solution is y t N m N sec m m N

16 Work Energy and Power 11 A spring is executing motion about equilibrium position x 0 where we take potential energy of spring to be zero The spring is oscillating between x and x position with a mass m attached During motion maximum speed of spring will be INCERT P 124 1 2 2 3 x 12 The graph between potential energy U of a spring versus its position x is best shown by graph equilibrium x 0 INCERT Pg 124 Ut 0 E U 0 x 13 Consider a situation in which a car of mass 2000 kg moving with speed of 54 km h on a smooth road and colliding with a horizontal mounted spring of spring constant 12 5 10 Nm What is maximum compression of INCERT Pg 124 2 6 m spring 1 4 m 3 8 m 4 1 m 14 An elevator can carry a maximum load of 900 kg elevator passengers is moving up with constant speed of 2 m s A constant frictional force of 5000 N opposes the INCERT Pg motion What minimum power is delivered by motor in HP 1 37 5 HP 3 42 5 HP 4 50 2 HP 15 Two objects with mass m 2 kg and m 3 kg collides perfect inelastically The particles were moving with speed of 10 ms and zero NCERT Pg 131 respectively before collision The loss of KE on collision is 1 60 J 2 40 J 3 100 J 4 90 J 16 Consider a collision between two identic billiard balls with equal masses m m First ball was at rest and second hits it edge Second ball after hitting mo ind Regd Office Aakash Tower 8 Pusa Re 17

Two bodies of masses 1 kg and 4 kg are connected to a vertical spring as shown in the figure The smaller mass executes simple harmonic motion of angular frequency 25 rad s and amplitude 1 6 cm while the bigger mass remains stationary on the ground The maximum force exerted by the system on the floor is take g 10 ms 2 1 20 N 3 60 N 2 10 N 4 40 N 1kg 4kg 2014

A body is simple harmonic motion with time period half second T 0 5 s and amplitude one cm A 1 cm Find the average velocity in the interval in which it moves from equilibrium position to half of it amplitude 2014 1 4 cm s 3 12 cm s 2 6 cm s 4 16 cm s

The student adjusts the pendulum so that d 50 0 cm She displaces the bob slightly and releases it so that it swings Fig 1 2 shows one complete oscillation of the pendulum She measures the time t for 20 complete oscillations i Record the time t shown in Fig 1 3 m S 100 00 28 12 Fig 13

4 there is no flow of air The bob of a simple pendulum executes simple harmonic motion in water with a period the period of oscillation of the bob is to in air Neglecting frictional force of water and giver density of the bob is x1000 kg m What relationship between t and to is true 1 t to 3 t 2to 3 2 t to 2 4 t 4to

20 A spring mass system of mass M natural angular frequency wo and damping constant g is driven at resonance by an external sinusoidal force F If the external force is increased by 16 times and the damping constant is reduced by 4 times the amplitude of the oscillation will O Increase by 4 times O Increase by 16 times O Increase by 64 times O Remain unchanged 1

A car is moving along a straight road with a uniform acceleration It passes through two points P and Q separated by a distance with velocity 30 km h and 40 km h respectively The velocity of the car midway between P and Q is A 33 3 km h B 20 2 km h C 25 2 km h D 35 km h

15 A mass M attached to a horizontal spring executes SHM with amplitude A When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A The ratio of is a c M m M A A 1 2 M m M b d M M m M M m 1 2

A 20 gm particle is subjected to two simple harmonic motions x1 2 sin 10 t x2 4 sin 10 t Where x X2 are in metre t is in sec 3 A The displacement of the particle at t 0 will be 2 3 m B Maximum speed of the particle will be 20 7 m s e Magnitude of maximum acceleration of the particle will be 200 7 m s D Energy of the resultant motion will be 28 J

27 A transverse sinusoidal wave of amplitude 2 mm is setup in a long uniform string Snapshot of string from x 0 to x meter is taken at t 0 which is shown Velocity of point P is in y direction Magnitude of relative velocity of P with respect to Q is 2 cm s Choose the correct options 1 mm y x 0 P upr A Displacement of particle at position P from its mean position as function of time is given by Y 2x10 sin5t m B wave equation is Y 2 x 10 sin 5t 2x m 6 C wave wave equation is Y 2 x 10 sin 5t 2x x 5T 6 m PHYSICS 5T VID wave equation is Y 2 x 10 sin 5t 2x m p 21h 1 1 O 0 A

27 29 3 12 2 3 min 2 3 33 A 4 0 53 A nstrained to move along y axis is jected to a constant force P 1 2 3KN The work done by this force in moving the body a distance of 4 m along y axis is 1 4 J 3 12 J 2 8 1 4 24 J The potential difference between A and B in the p Figure is 60 952 wwwwww 4V B P 1 0 53A 4 300 J translational KE 1 2001 2 100 3 3 150 J Figure shows the circular motion of a particle The radius of the circle the period sense of revolution and the initial position are indicated on the figure The simple harmonic motion of the x projection of the radias vector of the rotating particle P is X 50 www B 24 32 V 4 48 V wrizontal plane Its 1 What is its 25 ea Vavelength mer series 27 4 5 en height it hat fradtion 31 h bounce 4 narge and sitance will RF C 50 V C 43 V f a drop of given by tmospheric 29 n n8 1 4 R P It is in sec iis correct hertz city 300 m s axis 30 metre 32 33 14 4 x 1 B cos di atas al 1 0 20 Page 1 320 3 214 R 80 fins HAR GuF 4 F Sub 28 3 0 40 2 0 60 444 8 F 34allez il 2 51 e C 40 V C 27 N 40 V 7 F 9 F 28 3 4 G424141 HP 32411 412 API 8 2 420 u C 50 V 4 360 C 45 V 123 41 d Burundi ye TH 30 F 1 4R S 3 4R 4 nS sasa y 10 x 4 y 42241 47 Hy R 4 4m n4nR sin 60 t 2x 07 1 50 Hz X 2 ix l asasi 300 m s 2

Q10 A damped oscillations is executed by a mass of 400 g The spring constant is k 90 N m 1 and the damping constant b is 40 g s1 What is the time taken for its amplitude of vibrations to drop to half of its initial value Ma O A 15 25 s O B 20 79 s O c 6 93 s D 13 86 s

Aakash Educational Services Limited Regd Office Aakash Tower 3 All India Aakash Test Series for NEET 2021 vertical S H M If the amplitude at which the block 40 The time period 2 separate from the piston is of oscillation is 1 2 TU

Equation of a plane progressive wave is given y 0 6 sin2 t On reflection from a denser medium itsamplitude becomes 2 3 of the amplitude of the incident wave The equation of the reflected wave is 1 y 0 6sin2 1 2 3 y 0 4sin2 t y 0 4sin2 t 1 0 4sin2 1 x

4 0 782 s 13 The acceleration due to gravity on the surface of moon is 1 7 ms 2 What will be period of oscillation of a simple pendulum on the surface of moon if its time period on the surface of earth is 2s INCERT Pg 361 1 4 8 s 2 2 8 s 3 1 8 s 4 3 5 s A particle or 4 6 kg 16 The graph between length square of its time period best graph is Matic 1 2 L

In which of the following motions the time T will 7 have approximate value of 84 6 minute Mi a Time period T of a satellite revolving very close to the surface of the earth b Time period T of rotation of the earth so that a body kept on equator feels weightlessness Time period T of oscillation of an infinitely large simple pendulum C d Time period T of oscillation of a body along a complete tunnel through a chord of the earth 2 a b c and d 4 b and c 1 a b and c 3 a and b

20 On the superposition of the two waves given as Y A sin cot kx and Y A cost kx the resultant amplitude of oscillations will be 1 3A 2

3 A plastic cylinder of mass M and cross sectional area A is undergoing vertical SHM while floating in a liquid of density d The time period of oscillation can be increased by increasing 1 M 2 A 3 d 4 All of these otric

A particle is undergoing simple harmonic motion a time period of in a straight line with 3 3 second Starting from the mean position the oscillation will be completed in 9 second 80 3 1 25 second 2 1 second 4 0 75 second 8

View In English A mass M is suspended from a spring of 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 then the ratio of is M 1 rect Answer 3 Answer 2 us incorrect 3 5 25 9 16 9 5 W

Two springs with spring constants K and 2K are attached to a block of mass m and with fixed supports as shown When mass is displaced from equilibrium position on either side it executes SHM The frequency of oscillation is NCERT Pg 345 Imm Me 1 3 3m 2 V K 1 3m 2xV2K 2k 2 4 m 2n V2K 1 3K 2n V n m

9 The spring constants of two springs of same length are K and K as shown in figure If an object of mass M is suspended and set vibration the time period will be 1 2T MK K elle M VK K 3 2 M elle K 2 2 M K K 4 2 M K K

8 As shown in the figure two light springs of force constant K and K oscillate a block of mass M Its effective force constant will be 1 K K 1 1 3 K K mmmmmm K K M 2 K K K K 4 K K

81 Some springs are combined in series and parallel arrangement as shown in the figure and a mass M is suspended from them The ratio frequencies will be of their sheeeeeeee 3 3 2 K elle elle M elle 2 2 1 4 4 1 K son 019 2 ession

A body of mass m is hauled from the earth s surface by applying a force f 2 ah 1 mg where a is positive constant and h is height from the earth s surface A B At height h maximum At height h zero 1 the velocity of the body is 2a 1 a the velocity of particle is c The motion of particle is oscillatory int

6 The time period of mass suspended from a spring is T If the spring is cut into four equal parts and the same mass is suspended from one of the parts then the new time period will be 1 3 4 T 2 T 4 27

66 A mass m is at a distance a from center of a uniform rod of length I and M The gravitational force on the mass due to the rod is 4GMm 4GmM b a 1 4a 1 a c K GMm 2 a ERO d m 1 GmMO 2 1 a

Maximum 15 120 28 Displacement between maximum potential energy position and maximum kinetic energy position for a particle executing simple harmonic motion is 1 2 a 3 a 4 1 29 A particle of mass m oscillates with simple

A very long length L cylindrical galaxy is made of uniformly distributed mass and has radius R R L A star outside the galaxy in a plane perpendicular to the galaxy and passing through its centre If the time period of star is T and its distance from the galaxy s axis is r then 1 T cr3 2015 3 Toc r 2 Tor 4 T xc F

34 A mass m is vertically suspended from a spring of negligible mass the system oscillates with a frequency n What will be the frequency of the system if a mass 4m is suspended from the same spring 1 SIN ST 2 4n 3 4 2n 35 A mass is suspended separately by two different

Suppose that an oscillator has mass 1 X 10 7 g is attached to the surface of a solid by a bond having a force constant of 10 0 kg s 2 The maximum amplitude of this oscillator is 2 pm 1pm 10 12 m The total energy in joules of this oscillator when the amplitude 1pm and has a velocity of 1 105 m slis

are executing simple 6 Two particles harmonic motion of the same amplitude A and frequency along the x axis Their mean position is separated by distance X Xo A If the maximum separation between them is X A the phase difference between their motions is c 6 T 4 a T b d EN

128 Oscillations 21 A second s pendulum is mounted in a rocket Its period of oscillation will decrease when rocket is 1 Moving down with uniform acceleration 2 Moving around the earth in geostationary orbit

7 The variations of potential energy U with position x for three simple harmonic oscillators A B and C are shown in figure The oscillators have same mass The time period of oscillation is greatest for U U A 1 A 3 C B U C I 2 B 4 Same for all