Simple harmonic motion Questions and Answers

ET 12 The time period of a particle in simple harmonic motion is 8 s At t 0 it is at the I mean position The ratio of the distances travelled by it in the first and second seconds is 3 1 a 1 1 1 b 1 2 c 2 2 1 is mon The length of a pendulum d 1 3

4 The displacement of a particle executing SHM TC is given by y 5 sin 4t If T is the time 3 period and the mass of the particle is 2 g the T is kinetic energy of the particle when t given by a 0 4 J 4 b 0 5J c 3J d 0 3 J

resistance is 100 a inductive reactance at resonace condition 1 k After how many oscillation peak value 100 times maximum value current will fall to peak current 1 50 E TT 1 170053 2 100 the eh to e 3 50 t e 100 29 8 P

34 The equation of motion of a particle starting a 7 where x is in 3 t 0 is given by x 5 sin 20t centimeter and t is in second When does th particle come to rest for the second time 1 TO 10 3 7 S 120 2 4 7 T S 100 5T 7 S

30 A bullet of mass 0 02 kg moving with a speed of strikes a 2 kg wooden block suspended by a 1 m long thread and is embedded in the block What is the maximum inclination of the thread with the Ans 37 vertical g 9 8 ms 1 200 m s

23 The particle executing simple harmonic motion has a kinetic energy Kocos2 wt The maximum values of the potential energy and the total energy are respectively AIPMT Prelims 2007 1 K and K 2 0 and 2K Ko 3 and Ko 2 4 K and 2K 29 A part acting 1 A 2 A 3 4

A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle 20 The earth s magnetic field component in the direction perpendicular to swing is B The maximum potential difference induced across the pendulum is h 1 2BL sin 0 2 0 3 2 0 gL L 2 BL sin 2 gL 4 BL sin gL

28 Which of the following is simple harmonic motion 1 Particle moving in a circle with uniform speed 2 Wave moving through a string fixed at both ends art 3 Earth spinning about its axis 4 Ball bouncing between two rigid vertical walls 1 2 3 Zero 33 A linear h

A particle of mass 1 kg is undergoing SHM for which graph between force and displacement from mean position is shown Its time period in second is F N R 1 5 13 5 2 13 5 1 5 E TT x m

spring of 2 3 F block with longe the ation 27 1 2 K EX 3m 3 25K 1 2 g 2m 4 25K 3 2T 33 A particle of mass m is placed at lowest point of smooth parabola x ay What is the time period of small oscillation 9 dy Fans da 2a g 2 2 a 4g masi a 2g 4 2n T 2A du disc of mass m is connected to two shown Find time period a smooth

5 The displacement of a particle along the x a given by x a sin wt The motion of the particle corresponds to AIPMT Prelims 2010 1 Simple harmonic motion of frequency 3 R 3w 2 Simple harmonic motion of frequency 2 3 Non simple harmonic motion 4 Simple harmonic motion of frequency 2T

A small bob attached to a light inextensible thread of length I has periodic time T when allowed to oscillate as a simple pendulum The thread is now suspended from fixed end O of a vertical rigid wall 31 4 where the point of suspension is at a distance from the bottom end of wall as shown in figure If now pendulum performs simple harmonic oscillations in this arrangement the periodic time will be 1 3T 6 55 3 T 2 FIN F 2 4 2T

harmonic motion varies am 72 The displacements of the particle from extreme 3 A When angular amplitude position when its kinetic energy is th of the large then T 2m 3 maximum value and th of the maximum value are X and X respectively The ratio 1 3 1 2 1 2 3 1 3 4 2 3 1 XA XB is uin motro ond R Time period of simple angular amplitude f angular displacement 4 A If the elevator go acceleration then spring block sys independent of acc 5 R If the given elevat then the frequen A When the dar oscillating partic

ngle Correct Option 1 An insect of negligible mass is sitting on a block of mass M tied with a spring of force constanm The block performs simple harmonic motion with amplitude A in front of a plane mirror am shown The maximum speed of insect relative to its image will be b A 3 k reeee M 0 160 k c A 3 M d 2A M

rea of If it is brium Then 2006 eed 05 of 3 A particle of mass m is relea follows a parabolic path as shown Assuming that the displacement of the mass from the origin is small Which graph correctly depicts the position of the particle as a function of time v x 1 mwint emasa 3 4X t fr 4X t m 2 4 REALH 9 21 x 4X t 4x t 90 Asy on vax at

Stationary wave is represented by Y A sin 100 t cos 0 01 x where y and A are in mm t in sec and x in m The velocity of the wave 1 1 m s 3 104 m s 2 10 m s 4 not derivable

take x 3 00 g 10 m s 2 1 41 A spring of force constant k 300 N m connects two blocks having masses 2 kg and 3 kg on a smooth horizontal plane If the spring block system is released from a stretched position the number of complete oscillations in 1 minute Take 10 second

11 3 A C the particle is zero at t 0 1 s In the figure is shown a spring mass system oscillating in uniform gravity If we neglect all dissipative force how displacement x of the block from the equilibrium position varies with time t it will keep on oscillating endlessly with constant amplitude and frequency Accompanying graph shows unknown mechanism Which of the following graphs would correctly describes the changes taking place Now at a certain instant t t when the block reaches its lowest position gravity is switches off by some due to switching off the gravity A HARAM 000000000 AAAA AMMA M B D HAA

A block of mass 4kg attached with spring of spring constant 100 N m is executing SHM of amplitude 0 1m on smooth horizontal surface as shown in figure If another block of mass 5 kg is gently placed on it at the instant it passes through the mean position and new amplitude of motion is n meter then fin n Assuming that two blocks always move together m k Morros m

In the figure shown the spring are connected rod at one end and at the midpoint The rod is hinged at its lower end Rotational SHM of the rod Mass m length L will occur only if nie rok oldienst bowolls room 777 12 WOG 20 A k mg 3L C k 2mg 5Leinov k rom Ig 77 2009 leg bete dod lien 1928f1 B k 2mg 3L D k 0 What is the angular frequency of oscillations of the rod in the above problem ifk mg L A 3 2 k m 2 B 3 4 k m 2 1 511 2 Onu

Two light identical springs of spring constant k are attached horizontally at the two ends of an uniform B horizontal rod AB of length I and mass m The rod is pivoted at its centre O and can rotate freely in horizontal plane The other ends of the two springs are fixed to rigid supports as shown in figure A a The rod is gently pushed through a small angle and released The frequency of resulting oscillation is 1 2k 2n V m 6b b oooooo 1 3k 2 V m 1 k

In the figure shown mass 2m is at rest and in equilibrium A particle of mass m is released from height 4 5mg k from plate The particle sticks to the plate Neglecting the duration of collision Starting from the time when the particle sticks to plate to the time when the spring is in maximum compression for the first time is 2 then find a m ak E 00000 K 2

60 A particle performs S H M with frequency f of its velocity and acceleration are Frequency respectively 1 f f 2 f 2 3 2f f 4 f 2f

The acceleration due to gravity on the surface of moon is 1 6 ms 2 What is the time period of a simple pendulum on moon if time period on earth is 3 4 second Given acceleration due to gravity on earth 10 ms

20 In figure the spring has a force constant k The pulley is light and smooth the spring and the string are light The suspended block has a mass m If the block is slightly displaced from its equilibrium position and then released Find the period of its vertical oscillation E ooooo m

In the figure shown the spring are connected to the rod at one end and at the midpoint The rod is hinged at its lower end Rotational SHM of the rod Mass m length L will occur only if k 6ooooo00 k 60000000 Js

dilby 20 A bar magnet has a magnetic moment equal to 5x105 weber x metre It is suspended in a magnetic field which has a magnetic induction B equal to 8x10 4 tesla The magnet vibrates with a period of vibration equal to 15 sec The moment of inertia of the magnet is A 4 54 10 kg m B 4 54x10kg m C 4 54x10 kg m D 4 54 10 kg m Ifitis rotated by 600 the work done is 0 8 J How much

ustration 33 002 If a COP is cut into two equal parts then determine frequency of both part if initially it was n

D A cubical block of edge e and specific gravity 1 2 is in equilibrium with some volume inside water filled in a large fixed container Neglect viscous forces and surface tension The time period of small oscillations of the block in vertical direction is s T 2T 20

If the period of oscillation of particle performing simple harmonic motion is 8 s then the frequency of its kinetic energy will be 1 0 5 s 1 2 0 25 s 1 3 1 s 1 4 2 S 1

A 2 kg body panel of a car oscillates with a frequency of 2 Hz and amplitude 2 5 cm If the oscillations are assumed to be simple harmonic and undamped calculate the maximum velocity of the panel a b c d the total energy of the panel the maximum potential energy of the panel and the kinetic energy of the panel 1 0 cm from its equilibrium position

In superposition of two SHMs along x axis identify the correct options bold A IA A and 8 the particle is always at rest B If 8 0 A A and o o then the resultant motion is a harmonic motion with angular frequency 1 2 2 C If A A 0 8 0 and A A then the 2 3 A particle is at origin at time t 0 02 D IfA A o co and 8 0 then the amplitude of 2 resultant SHMia

Example 9 A particle of mass m is attached with three springs A B and C of equal force constants k as shown in figure The particle is pushed slightly against the spring C and released Find the time period of oscillation 45 wwwwww C B 90 www

28 A general graph showing variation in potential energy PE of a particle with time while executing S H M is 1 PE 3 time 2 PE m m m PE time 4 PE time 132 A time

In the AC circuit the current is expressed as 100 sin 200mt In this circuit the current rises from zero to peak value in time 1 3 1 400 1 00 S S 1 2 S 300 4 1 200 S

A small body of mass 10grams is making harmonic oscillations along a straight line with a time period of 4 and the maximum displacement is 10 cm The energy of oscillator is

A particle of mass 2kg moving on a straight line under the action of force F 8 2x N It is released from rest at x 6 then time period is 1 A second 2 47 second 4 2 second 2 20 second

The length of weight less spring Increases by 2cm when weight 1 0kg is suspended from it The weight is pulled down by 10cm a released Determine 1 Period of oscillation of the spring Maximum K E of oscillation of the spring

2 A highly rigid cubical block of mass m and side L is fixed rigidly on to another cubical block B of the same dimensions and of low modulus of rigidily n such that the lower face of A completely covers the upper face of B The lower face of B is rigidly held on a horizontal surface A small force F is applied perpendicular to one of the side faces of A After the force is withdrawn block A executes small oscillation the period is a 2n nmL ben c 2T V mL n b 2 m d 2 111 nl

A magnet is suspended from a spring and when it oscillates the magnet moves in and out of the coil C The coil is connected to a galvanometer G Then as the magnet oscillates 1 G shows no deflection 2 G shows deflection to the left and right but the amplitude steadily decreases 3 G shows deflection to the left and right with constant amplitude 4 G shows deflection on one side

Two particles undergo SHM along parallel lines with same time period T and equal amplitudes At a particular instant one particle is at its extreme position while the other is at its mean position They move in the same direction They will cross each other after a further time 1 3 1100 96 T 2 4 15100 3T 4T 3

The minimum time taken by a body executing simple harmonic motion in which its speed decreases by half its maximum speed will be T time period 1 3 916 T T 2 4 T 4 T 8

momaisi2 2205 A certain ideal spring stretches 20 cm when m 40 gm mass is hung from it If a mass of gm gm is hung instead of 40 gm at its end pulled out 20 cm from equilibrium and released at t 0 sec Choose the correct option s g 10 m s m 32 A The magnitude of acceleration of the m mass when it is 2 5 cm from the equilibrium position 64 m s is 45 nor esona B The magnitude of acceleration of the m mass when it is 2 5 cm from the equilibrium position 32 is m s 45 T C At t sec m mass is 10 cm from equilibrium position sin al 8 T D At t sec m mass is 10 cm from equilibrium position 2 smaisia ART 6 18 0

If y 5 mm sinnt is equation of oscillation of source S and y2 5 mm sin xt 6 be that S and it takes 1 sec and sec for the transverse waves to reach point A from sources S and respectively then the resulting amplitude at point A is A A 5 2 3 mm S B 5 3 mi mm C 5 mm S D 5 2 mm

The displacement x in metre of an oscillating particle varies with time t in second according to the equation TU x 0 02 cos 0 5t 3 Calculate a amplitude of oscillation b time period of oscillation c maximum velocity of particle d maximum acceleration of particle

A solid sphere m kg R meter placed on a horizontal rough plane is attached to a spring S fixed to a light rod OA of length L meter as shown in the figure The other end 0 of the rod is hinged to rotate in the plane about vertical axis passing through it A spring S is fixed to the midpoint B of the rod If the spring constants of both springs are N each then the angular frequency of oscillations of the mass would be in rad s 1 2 3 4 k 7m 11k 28m 2k 7m 2k Sm S Arm B 0 xx

equil P Q 25 R S odes P2 ods of oscillation are given in List II List I R 21 A solid sphere of mass m and radius R are connected with two springs friction is sufficient to present slipping Now solid sphere is slightly displaced then its time period is 2k vooroos 03 Q R 1 k 888888 A block of mass m is connected with two springs and a mass less pulley Now is block is slightly displaced from its equilibrium position then its time period is 4k k S 4 eeeeeee A block of mass m is connected with three springs and a massless pulley Surface is smooth and block is slightly shifted toward right then its time period is k eeeeeee k wwwww Masses of pulley and blocks are m and friction is sufficient to prevent slipping between string and pulley Now block is slightly displaced then its time period is eeessee k www k 0000000 rigid bodies shown are 1 2 3 4 TC List II m 6k 2 2 20 T 2m k 28m 45k 5m k A kxx E 2k

For a simple harmonic oscillator of mass m 10 kg and amplitude A 2 m the variation of potential energy U as a function of displacement x from mean position is as shown The time period of oscillation in second is A 1 T 3 ww KIN U 0 30 J 10 J A 2 2 4 4 New Ch 3 17

A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x 2 sin oot y 2 ot The path of the particle will be 4 sin A an ellipse Mizow C a parabola B a straight line D a circle

A block of mass m is placed on a smooth horizontal floor is attached to one end of spring The other end of the spring is attached to fixed support When spring is vertical it is relaxed Now the block is pulled towards right by a force F which is being increased gradually When the spring makes angle 53 with the vertical block leaves the floor relle