Simple harmonic motion Questions and Answers

A book with many printing errors contains four different formulas for displacement y of a particle undergoing a certain periodic motion a y a sin 2x t T the b y a sin vt c y a T sin t a d y a 2 sin 2xt T cos2xt T

2 An object in a frictionless horizontal plane is attached to the wall by a spring The object was released by pulling 10 cm from the equilibrium position m 1 kg k 1000 N m a Calculate the potential energy and kinetic energy of the object as it passes through the equilibrium position b Calculate the potential energy and velocity of the object as it passes 6 cm reeeee E x 0

20 A particle is subjected to two simple harmonic motions both along x axis which are given by X 5sinot and x2 5sin particle will be 1 An ellipse 3 A hyperbola francuerco WOWO ot The path of 2 2 A straight line 4 A circle which is travelling along

An object in simple harmonic motion takes 0 250 second to move from its equilibrium position to its maximum displacement y 5 cm The maximum velocity of the object is y 5 cm y 0 y 5 cm t 0 25 s 5 cm s 10 cm s 25 cm s 10 cm s

3 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 5 103 Nm 1 What is maximum compression of spring NCERT Pg 124 1 4 m 26m 3 8 m 4 1 m An elevator can carry a maximum load of 900 kg elevator passengers is moving up with constant speed of 2 m s 1 A constant O m 1 1 53 3 37 17 In a nuclea 104 m s

A hollow sphere is filled with water It is hung by a long thread to make it a simple pendulum As the water flows out of a hole at the bottom of the sphere the frequency of oscillation will Go on increasing Go on decreasing First increases and then decreases First decreases and then becomes equal to initial value

Consider the situation shown in the figure The spring force constant k is ideal and the surface is frictionless Each block is given displacement of smal magnitude xo in opposite directions and released simultaneously from rest for the subsequent motion choose the correct statement s 2m A m k oooooo B Smooth Amplitude of motion of block A is 20 3 Amplitude of motion of block Bis 2x0 Frequency of oscillation of block Bis

The amplitude of a damped oscillator decreases to 0 9 times its original magnitude in 5s In another 10 s it will decrease to a times its original magnitude where a equals 1 0 7 2 0 81 3 0 729 4 0 6

Q No 9 A solid cylinder of mass 50 kg and radius 0 5 m is free to rotate about the horizontal axis A massless string is wound round the cylinder with one end attached to it and other hanging freely Tension in 2 the string required to produce an angular acceleration of 2 revolutions s is CATE Correct Answer 4 Your Answer 1 25 N 50 N 78 5 N 157 N

1 4 3 4 2 39 If amplitude of the particle which is executing S H M is doubled then which quantity will remain same 1 Frequency 2 Total energy 3 Maximum acceleration 4 Maximum velocity C

A uniform rod is placed on two spinning wheels as shown in figure The axes of the wheels are separated by a distance 50 m the coefficient of friction between the rod and the T wheels is 0 1 The rod performs harmonic oscillations The period of these oscillations is 10x sec Find the value of x

A circuit has an inductance of 10 mH capacitance 0 1uF and resistance 1k connected to a DC source Circuit is A critically damped B over damped C periodic with damping OD periodic

rticle is 16 cm s mean position at mes 8 3 cm sec 8 A block is resting on a piston which is moving vertically with SHM of period 1 sec At what amplitude of motion will the block and piston seperate a 0 2 m b 0 25 m c 0 3 m d 0 35 m

A smooth fixed rod is inclined at an angle 30 to horizontal There is a fixed charge Q at the bottom of rod There is a bead of mass m having charge q that can slide freely on the rod At equilibrium height of bead is Time period of oscillation of bead is Q 30 O 2 t O 2 2 h 12g 12h a q h 2

A block of mass moving vertically in an SHM of period motion at which the block and piston separate is g 0 0 25 m O 0 52 m 025m 0 0 15 m

A spring pendulum oscillates in a vertical plane such that the time period of the oscillation is T If the whole setup is hung from ceiling of an elevator moving up with an acceleration then the time period of oscillation of the spring will be OT 72 O2T

simple pendulum of length has maximum angular displacement 0 The maximur netic energy of the bob of mass m is g acceleration due to gravity mg 1 cos0 B mg 1 cos 0 C mg 1 cos0 D mg cos0 1

Two similar thin bars AB and OC of mass 1 2 kg and length 9 34 m are joined to form an inverted T The system of 2 bars is hinged at O such that it can rotate freely about a horizontal axis through O and perpendicular to plane of paper The bar OC is slightly displaced from the vertical and released The period of oscillation in sec is

2 3 ct Answer 1 Answer 4 E incorrect 21 21 21 10 to Bookmark List Peer Stat Unattempted 31 9 Correct 52 6 Incorrect 155 positions After how much tim

One end of a spring of force constant kis fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface There is another wall at a distance to from the black The spring is then compressed by 2x0 and released The time taken to strike the wall is 0000000 M

A particle of mass mis attached to a spring of spring constant k and has a natural angular frequency wo An external force F t proportional to cos w t w applied to the oscillator The time displacement of the oscillator will be proportional to wo is Answer Your Attempt Rate this question Correct answer

If the displacement of a particle executing SHM is given by y 0 25 sin 200t 0 8 in S units Its maximum velocity is 1 50m s Two S H M s are represent The no 2 100m s 3 25m s 4 200m s

Two mutually perpendicular simple harmonic vibrations of the same frequency superimpose on each other The amplitude of the two vibrations is different and they are different from each other in phase The resultant of superposition is 1 Parabola 2 Straight line 3 Elliptical 4 Circular

A mass M attached to a spring oscillates with a period of 2 s If the mass is increased by 2 kg the period increases by one sec Find the initial mass M In kg assuming that Hooke s Law is obeyed EXPLANATION Correct Answer 1 6

A mass of 30 gm is attached with two springs having spring constants 100 N m and 200 N m and other ends of springs are attached to rigid walls as shown in the given figure The angular frequency of oscillation is Ground is smooth 1 2 100 2T 100 rad s rad s 3 100 rad s 4 200m rad s 100 Nm Foo wwwwwwww 200 Nm vvvvvvvvv

wo massless springs of stiffness K each are connected from a vertical wall to a block of mass m The inclination of each spring with the horizontal surface is 8 For oscillations of small amplitude of the block over the smooth horizontal surface what is the time period of oscillations ok

For a stretched string the parameters are given as length 0 80 m total mass 0 32 g and tension T 280 N Find the first harmonic of the string when plucked O 523 Hz 1046 Hz 262 Hz 131 H 2 p

Two massless springs of stiffness K each are connected from a vertical wall to a block of mass m The inclination of each spring with the horizontal surface is 8 For oscillations of small amplitude of the block over the smooth horizontal surface what is the time period of oscillations K K 0 m

questions 17 18 A particle of mass m moves in x y plane under the action of a force with components F mk 2x y F mk x 2y where k is a constant Find the possible angular frequencies of SHM along 2 possible directions k for both 3k and k 2k and k 2 2k and k

A system consists of two identical cubes each of mass m linked together by the con pressed weightless spring of stiffnes x The cubes are also connected by a thread which is burned through at a certain moment If the initial compression of the spring is h Nmg X find N 7mg X then the centre of gravity of this system will rise by height

A mass m 8 kg is attahced to a spring as shown in figure and held in position so that the spring remains unstretched The spring constant is 200 N m The mass m is then released and begins to undergo small oscillations The maximum velocity of the mass will be g 10 m s reeeeeee m 1 1 m s 2 2 m s 3 4 m s 4 5 m s

1 Following graph shows a particle performing S H M about mean position x 0 The equation T is taken as starting time is Notations have usual meanings particle if t A A sin cot 27 3 B A sin oot T C A sin ot D A cost cos ot 2 t 3

springs of spring constants k and k separately executes simple harmonic motion During oscillation the maximum velocity is equal in both cases The ratio of amplitude A A is M GWH on Ych des Acifad slche yuch quch at K K 4 Hem 31 d na aka dai Refaut 3f chau au CRIER stai at 44 A m A2 A K B k k

A particle is acted simultaneously by mutually perpendicular simple hormonic motions x a cos wt and y a sin wt The trajectory of motion of the particle will be Question Type Single Correct Type 1 2 3 an ellipse a parabola a circle

Two pendulums of time periods 3s and 7s start oscillating from two opposite extreme positions After how much time they will be in phase respectively simultaneously Question Type Single Correct Type 1 2 21 8 S 2014042 S

e Which of the following system has have time period T are ideal and surfaces are smooth A M 000000000 m 2k 000000000 m B D k eeeeeeeee e k m m for small oscillation pulley

A particle of mass 4gm is moving simple harmonically with a period 8 sec and amplitude 8cm What is its velocity when its displacement is 8 cm 1 8cm 2 6cm 3 4cm For a body in S H M the velocity is given by the laund 4 zero

1 1 3 sec 2 1 4 sec 3 1 2 sec Two simple harmonic oscillators with amplitudes in the ratio 1 2 are having the same total energy The ratio of their frequencies is 1 1 4 4 4 1 2 1 2 3 2 1

1 2 2 T 3 2 3 The maximum speed of a particle in S H M is found to be 62 8 cm s If the amplitude is 20 cm its period of oscillation is 1 1 sec 2 2 sec 3 3 sec 4 4 sec displacement will be half the amplitude

5 The equation of motion of a particle is given by dP mo n 0 where P is the momentum dt 98E 2 Moves along a parabola 4 Falls freely under gravity and n is the position Then the particle 1 Moves along a staight line 3 Executes SHM moss 100gm when its amplitude is 1 is

3 4 3 4 3 4 The displacement equation of a simple harmonic oscillator is given by T 8 12 m Its displacement when t 2 second is 3 3 3 m X 6 sin TU t 1 3m A particle of mass d 2 1 5m 4 3 2m

cm 3 4cm 4 zero For a body in S H M the velocity is given by the relation V 144 16x ms The maximun acceleration is 1 12m s 2 16 m s A paticle is executing S H M of amplitudo n 3 36 m s 4 48 m s

1 1N A body of mass 1 4 kg is in S H M Its displacement is given by the relatio y 0 05 sin 20t 2 m If t is in seconds the maximum force acting on the particle is 3 10N 01 4 0 25N 1 5N 2 2 5 N

4 200m s 3 25m s Two S H M s are represented by the relations x 4 sin 80t n 2 and y 2 cos 60t 2 The ratio of their time periods is 1 2 1 2 1 2 The displacement equation of a simple l 2 100m s 3 4 3 4 3 4

The equation of nation of a particle executing SHM is a 16 x 0 In the equation a is the liner acceleration in m s2 of the particle at a displacemtn x in metre The time period of SHM in seconds is 2 3 1 4 2

In the SHM the ratio of frequency of oscillation KE to that o velocity v is 1 2 2 1 4 1 E 1 4

When a particle perform simple harmonic motion then its TII Velocity continuously change and acceleration remain constant Velocity and acceleration change continuously Velocity remain constant and acceleration continuously change Velocity and acceleration does not change

When a mass m is hung from the lower end of a spring of negligible mass an extension x is produced in the spring The mass is set into vertical oscillations The time period of oscillation is T 2t T 2 T 2 mg gx m T 2 65

A particle of mass 1 kg is undergoing S H M for which graph between force and displacement from mean position as shown time period in seconds is F N 1 5 13 5 www FI6 13 5 1 5 x m

A particle performs SHM with an amplitude A The displacement of the particle from the mean position where the kinetic energy of the particle and the elastic potential energy are in the ratio 1 2 respectively A 2A 23 3 A