Simple harmonic motion Questions and Answers

View In Engl child with poor table manners is sliding his dinner plate back and forth in SHM with an amplitude of 10 cm on a horizontal surface At a point 6 cm away from equilibrium the speed of the ste is 40 cm s What is the period Os 5 2T

4 A simple pendulum performs simple harmonic motion about x 0 with an amplitude a and time period T The speed of the pendulum at x a 2 will be na 3 3 d T 2T a T b 37 a T c 5 A mass of 2 0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure The mass of the spring and the pan is negligible When pressed slightly and released the mass executes a simple 2009 elleeeeeee m harmonic motion The spring constant is 200 N m What should be the minimum amplitude of the motion so that the mass gets detached from the pan take g 10 m s a 10 0 cm b any value less than 12 0 cm

A bob of a simple pendulum has mass m and is oscillating with an amplitude a If the length of the pendulum is L then the maximum tension in the string is cos 0 1 g acceleration due to gravity mg 1 mg 1 mg 2 P m 1 1 D mg A B C

A man of mass M is standing on the platform The platform is executing S H M of frequency f in vertical direction The span of oscillation is L Then the acceleration of the platform at the top of the oscillation is 4 f L A B C 2 f L M 4 f L M

42 A body of mass m is attached to the lower end of a spring whose upper end is fixed The spring has negligible mass When the mass m is slightly pulled down and released it oscillates with a time period of 3 s When the mass m is increased by 1 kg the time period of oscillations becomes 5 s The value of m in kg is 3 a 4 b 3 c 16 9 9 16 NEET II 2016 d 43 The period of oscillation of a mass M suspended from a spring of negligible mass is T If along with it another mass M is also suspended the period oscillation will now be H T a T b c 2T T d 2T

0 A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator The acceleration of the bob of the pendulum is 20 m s at a distance of 5 m from the mean position The time period of oscillation is a 2 s b Ts c 2 s d 1 s

A particle executes simple harmonic motion with amplitude A and period T If it is half way between mean position and extreme position then its speed at that point is A B C 3 T 3 TA 2T T

For a particle performing S H M when displacement is x the potential energy and restoring force acting on it is denoted by E and F respectively The relation between x E and Fis OF A B2E F C x x 0 D F 2E x 0 x 0 X 0

15 A particle is executing a simple harmonic motion Its maximum acceleration is a and maximum velocity is Then its time period of vibration will be B 2 B a b O a B c a d 2015

Two bodies A and B of equal mass are suspended from two separate massless springs of force constant ki and ka respectively The bodies oscillate vertically such that their maximum velocities are equal The ratio of the amplitudes of body A to that of body B is A B C D k K2 k k

A pendulum performs S H M with period 3 second in a stationery lift If lift move up with acceleration the period of pendulum is g acceleration due to gravity A B C D 2 00 second 1 5 second 2 5 second 1 75 second

A coin is placed on the horizontal plate Plate performs S H M vertically with angular frequency o The amplitude A of oscillations is gradually increased The coin will lose contact with plate for the first time when amplitude is acceleration due to gravity A B C D g 2013 zero w 8 0 g A 2

For a particle executing SHM the displacement x is given by x A cos wot Identify the graph which represents the variation of potential energy PE as a function of time t and displacement x 2003 2M O PE xxxxx b II IV a I III c II III PE X d I I

42 Two identical blocks A and B are connected with a spring of constant k as shown in figure If block B is moving rightward with speed v then the maximum extension of spring is 1 2 m 5000000 th Smooth 2 2k

no 21 10 A block of mass 2 kg is redeased from the top of an inclined smooth surface as shown is figure If spring constant of spring is 100N m and block comes to rest after compressing the spring by then the distance travelled by block before it comes to rest is kg 1 Im 2 1 25m 3 2 5m 4 5m 121 0 0 0 00 mal 8 DPP O digoned from roso 450 a height ho lilher loss

5 The displacement of a particle along the x axis is given by x asin oot The motion of the particle corresponds to a simple harmonic motion of frequency w b simple harmonic motion of frequency 300 2 c non simple harmonic motion d simple harmonic motion of frequency 2 201

Two identical balls A and B each of mass 0 1 kg are attached to two identical massless springs The spring mass system is constrained to move inside a rigid smooth pipe bent in the form of a circle as shown in the figure The pipe is fixed in a horizontal plane The centres of the balls can move in a circle of radius 0 06 m Each spring has a natural length of 0 067 m and spring constant 0 1 N m Initially both the balls are displaced by an angle rad with respect to the diameter PQ of the circle as shown in the figure and released from rest The frequency of oscillation of balls is P A 1 B 2 1555 3 A Am eeeee Hz Hz Hz 100000 Hz TT 6 oooooo 0 06 m TT 6 B 100000 hell e o o o ele e e

16 Two large conducting plates having surface 3 charge densities G and respectively are fixed d distance apart A small test charge q of mass m is attached to two identical springs as shown in the adjacent figure The charge q is now released from rest with springs in natural length Then q will neglect gravity 0 TOWY km k THIE d B 1 perform SHM with angular frequency Telegram ne questionpaper 9 2 perform SHM with amplitude 2k m 3 not perform SHM but will have a periodic motion 4 remain stationary fram fe fanger tr 0 AL a farmer 9 mor TAIT kmk d 9 far i araferen B 1 Red fantom ferred vita nafa 2 tom foren ara 3 4 FI m 81 2k siera fat

A block of mass m attached to one end of the vertical spring produces extension x If the block is pulled and released the periodic time of oscillation is A B C 2 T D 2x g 2 T 2 T 2 T 5 0 XI 6 0 X 2g X

A body of mass 64 g is made to oscillate turn by turn on two different springs A and B Spring A and B has force constant 4 and 16 respectively If T and T2 N N m m are period of oscillations of springs A and B respectively then A B C 1 3 3 1 1 2 T T T T 2 1 will be

A particle of mass m is moving in a potential of the form V x y z 1 2 mw 3x 3y 2z 2xy The oscillation frequencies of the three normal modes of the particle are given by b 20 30 and 300 d 2w 20 and 2w a w 3w and w c 2w 2w and 2w

When a mass m is suspended from a spring of length e the length of the spring becomes L The mass is pulled down by a distance d and released If the equation of motion of the mass is P x 0 then P is equal to dt g acceleration due to gravity L l A B C g g L l g L l L l

Q 8 The velocities of a particle in SHM at positions x and x are v and v2 respectively its time X1 v1 period will be 1 2n 0 0 x 2 x x x v v 3 2 2 2n 4 2 x x 2 2 0 32 0 2 x x V 2 71

equilibrium position x 0 270 m 70000 voooo X 0 Find the effective spring constant of the system Submit Answer Tries 0 12 The glider is now released from rest at x 0 270 m Find the maximum x acceleration of the glider Submit Answer Tries 0 12 Find the x coordinate of the glider at time t 0 370T where T is the period of the oscillation Submit Answer Tries 0 12 Find the kinetic onoray of the glider at v 2

The point A moves with a uniform speed along the circumference of a circ of radius 0 36 m and covers 30 in 0 1 s The perpendicular projection P from A on the diameter MN represents the simple harmonic motion of P The restoration force per unit mass when P touches M will be A 9 87 N B C 0 49 N 50 N 100 N M 0 36 m 30 P 0 1 s N

The time period of mass M when displaced from its equilibrium position and then released for the system as shown in figure is 1 2 3 4 Correct Answer 3 2T 21 MERME 2k 24K 2M 21 k Inextensible string 00000000 pulley M

Two particles execute SHM of same amplitude of 20 cm with same period along the same line about the same equilibrium position The maximum distance between the two is 20 cm Their phase difference in radians is B 1 1 2 A 2 3 Se 3 D e 4

A simple pendulum of length l has a bob of mass m It executes S H M of small amplitude A The maximum tension in the string is g acceleration due to gravity A 2 mg B C D mg mg mg 1 1 2 1 2

A particle of mass m is attached to three identical springs A B and C each of force constant k as shown in figure If the particle of mass m is pushed slightly against the spring A and released then the time period of oscillation is ellele B 90 0lm A rellele mmmmm

11 A particle performing SHM is found at its equilibrium at t 1 sec and it is found to have a speed of 0 25 m s at t 2 sec If the period of oscillation is 6 sec Calculate amplitude of oscillation A C V Aw sin art 3 2 O E m m 3 B m 4 3 8 D

A longitudinal harmonic wave is travelling along positive x direction The amplitude wavelength and frequency of the wave are 8 0 x 103 m 12 cm and 6800 Hz respectively The displacement s versus position graph for particles on the x axis at an instant of time has been shown in figure Find the separation at the instant shown between the particles which were originally at x 1 cm and x2 3 cm separation in given in cm hs X

A particle performs SHM with a period T and amplitude a The mean velocity of the particle over the time interval during which it travels a distance a 2 from the extreme position is A a T B 2a T C 3a T D a 2T particle performing SHM to

The equation of particle executing simple harmonic T motion is x 5m sin s t Write down 3 the amplitude time period and maximum speed Also find the velocity at t 1 s

Two plates of same mass are attached rigidly to the two ends of a spring One of the plates rests on a horizontal surface and the other results a compression X of the spring when it is in steady state To lift off the lowest plate after removing the force What further compression is required 1 0 5X 2 3X ITTT T 600000000 m

A particle moves with simple harmonic motion in a straight line In first ts after starting from rest it trave a distance a and in next ts it travels 2a in same direction then 1 amplitude of motion is 4a 3 amplitude of motion is 3a 2 time period of oscillations is 6t 4 time period of oscillations is 8t

TOO A simple pendulum is suspended in a uniform electric field E as shown in the figure What will be its period if its length Charge on the bob of pendulum is q and mass is m is Ans T 2 1 2 9 E 28qE cose 8 2 m m

A uniform rod of length L 60 cm is suspended through an end and is set into oscillation with small amplitude under gravity Find the time period of oscillation g 10 m s A B 0 4 S 0 2 TS 0 4 s 0 2 s

Q The ends of a rod of length L and mass m attached to identical spring rod free to rotate about centre O The rod s depressed slightly at A and released Time period of osci lation is 119 110mm 2115 min 315 min 4 V min 27 The ends of a rod of length I and mass mare attached to two identical springs as shown in the figure The rod is free to rotate about its centre O The rod is depressed slightly at end A and released The time period of the oscillation is 1

diagram and pls explain solution in easy and understanda le way A 2 kg block moving with 10 m s strikes a spring of spring constant N m attached to 2 kg block at rest kept on a smooth floor The time for which rear moving block remain in contact with spring will be 10 m s 2 kg m 2 kg 2 S 31 1s S

A particle of mass m is executing simple harmonic motion about its mean position If A is the amplitude and T is the period of S H M then the total energy of the particle is A B C D 4 m T 8 m T 2 m T m

A particle performs S H M from the mean position Its amplitude is A and total 3E energy is E At a perticular instant its kinetic energy is The displacement of the 4 particle at that instant is A B C D A AL8 A 4 D A

Three students S S2 and S3 perform an experiment for determining the acceleration due to gravity g using a simple pendulum They use different lengths of pendulum and record time for different number of oscillations The observations are as shown in the table Student No 123 3 Length of No of Pendulum cm 64 0 64 0 20 0 oscillations n 8 4 4 Total tim for n oscillation 128 0 64 0 36 0 Least count of length 0 1 cm and Least count for time 0 1 s If E E2 and E3 are the percentage errors in g for students 1 2 and 3 respectively then

Which of the following is correct about a SHM along a straight line ONO No Ratio of acceleration to velocity is constant Ratio of acceleration to potential energy is constant Ratio of acceleration to displacement from the mean position is constant

In a horizontal spring mass system mass m is released after being displaced towards right by J some distance t 0 on a friction less surface The phase angle of motion in radian when it is first time passing through equilibrium position is equal to k m

Two different simple harmonic oscillators have the same natural frequency f 2 60 Hz when they are on the surface of the Earth The first oscillator is a pendulum the second vertical spring and mass If both systems are moved to the surface of the moon g 1 67 m s2 what is the new frequency of the pendulum Submit Answer Tries 0 20 Calculate the new frequency of the vertical spring and mass

A particle of mass 2 kg is moving along a line due to a force F 5x 6 where x is the instantaneous position The particle will perform 1 SHM about x 6 V5 5 2 2 SHM with angular frequency 3 Translational motion with a constant acceleration with a variable acceleration

34 The block is released after stretching the spring by a distance A from its natural length The graph which represents the velocity of the block will be 1 3 K vooooooooo m smooth X axis NA t 2 t 4 t

The figure present an arrangement in horizontal plane It consists of a parallel plate capacitor with one of its square plate fixed by means of an insulating support While the other plate is attached to the free end of a spring made of insulating material of force constant K If the capacitor carries charge Q and battery is disconnected mass and side length of plate A be M and L respectively time period of oscillation of A assuming that it does not strike B would be ignore any friction A B mtum K US14

A particle is suspended by two identical strings as shown in the figure Now mass m is given a small displacement perpendicular to the plane of the triangle formed Choose the correct statement s yc cu ch faa seny ggar A464 Jkut A Achu nu 1 H wha m Affa Ayu u faz u km 4 21 43 543 CYCH A 2 B 2 5 71 C m 3 21 The period of oscillations of system is 3 31 9 A 2 3 31 g The period of oscillations of system is 310 g A 2 Correct Answer 31 9 The period of oscillations of system is Correct Answer independent of mass m Ac Kad Kid GWH3 m uz A4 75 D If the distance between the suspension points was kept constant and the length of the strings were quadrupled then the time period will be doubled uf Adda fa ut qwu a s Aua zu Ga Rutas ct atya fu

A particle of mass m executes SHM with amplitude a and frequency n The average kinetic energy of particle is one complete oscillation is 1 4 ma n 2 27 ma n 3 ma n I 1 4 ma n A