Simple harmonic motion Questions and Answers

Q No 19 Sections Measuring mechanism whose mobile component attains its equilibrium position without oscillations round new position is called A Damped measuring mechanism B Aperiodic measuring mechanism C Stable measuring mechanism D Precise measuring mechanism

The damping force on an oscillator is directly proportional to the velocity The units of the constant of proportionality are AIPMT Prelims 2012 1 kg s 1 2 kg s 3 kg ms 1 4 kgm s 2

The time period of a givel K dddddd Spring 2 m LEIX T 2 1 2K 10 Block 2 1 m Elastic string Solution Answer 3 When a string is compressed then it does not provide any restoring fo Hence T T T2 22 2x m 2 2k m Jm 1 k 2x m 2 k m 2 1 2K

Consider the system of solid cylinder and plank connected with spring and placed on sufficiently rough surface If m 1 1 kg and k 100 N m Find time period of small oscillation in ms Take 3 14 00000000 k m m R k 00000000

wo masses m and m are joined by a spring as shown The system is dropped to the ground from a certain height The spring will be 1 Stretched when m m 2 compressed when m m 3 neither compressed nor stretched only when m m 4 neither compressed nor stretched regardless of the values of m and 500000 m

Q 8 A solid cone of semi vertical angle a 30 and height h is suspended vertically from its vertex as shown in the figure The cone is slightly rotated from its vertical position and then released If the time period of small oscillations of the cone is 2 k 13h 45g Find the value of k Your Answer Rate this questi

21 The period of oscillation of simple pendulum is 1 measured value of Lis 20 0 cm known to T 2 V g 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1s resolution What is the accuracy in the determination of g a 3 2 Find the resultant b 1 4A of il c 5 d 2

1 For the two adiabatics shown on a pressure volume P V diagram if process 1 is for oxygen gas then process 2 may be for Assume all gases are ideal 1 N PA Tal V 2 CO 4 O

A block of mass m 1 kg is attached to a spring of force constant k 24 N cm at one end and attached to a string tensioned by mass m 5 kg Deduce the frequency of oscillations of the system If m is initially supported in hand with spring unstretched and then suddenly released find instantaneous tension just after m is released the maximum displacement of m 0 the maximum and minimum tensions in the string during oscillations stayyo m FIFTIE m

A block of mass m which can slide up and down without rotation between two frictionless walls is suspended with the help of two light springs and a light inextensible cord that passes over an ideal pulley as shown in the figure Force constants of the springs are k and k If the bar is pulled down slightly and released it will oscillate up and down Find period of these oscillations

A particle is moving with constant angular velocity w along a circular path of radius A as shown in figure Find out x component of velocity of particle as a function of time 1 2 Question Type Single Correct Type 3 4 0 0 30 v Aw cos wt 6 v Aw cos wt v Aw cos wt 6 v Aw sin wt 6 X

1 0 8 and 49 2 0 9 and 90 3 0 7 and 50 4 0 99 and 99 5 The simple harmonic motion of a particle is 35 36 I represented by the equation x 4 cos 88t The frequency in Hz and the initial position in m of the particle are 1 14 2 2 2 16 2 2 3 14 3 2 4 16 3 2 A halloon of mass m is descending down with an 36 1 0 8 and 49 3 0 7 and 50 at matt 2 0 9 and 90 4 0 99 and 99 SUI GRI ZED 1 14 2 2 3 14 3 2 x 4 cos 88t 3 m GHG n von To fff 2 16 2 2 4 16 3 2 an air

time period 2 g 57 Consider one end of an ideal spring with spring constant K fixed and other end is attached to a block of mass M placed on a smooth horizontal surface After stretching the spring by length Al and releasing it the instant the spring regains its natural length few drops of molten wax of total mass 3 on the block which sticks to it The stretching of the spring hence will be 1 Al 3 Al 3 2 2 M 4 3Al 2 2Al 3 is dropped maximum mass M passe smaller mass m is move together with A is 63 M 1 M m M 3 M m k 8000000 A cylinder of n

Two particles carrying charges q and q and having equal masses m each are fixed at the ends of a light rod of length a to from a dipole The rod is clamped at an end and is placed in a uniform electric field E with the axis of the dipole along the electric field The rod is slightly tilted and then released Neglecting gravity find the time period of small oscillations Question Type Single Correct Type 1 2 mq 4 V qE 2 2 3 2 m qE m

An ideal gas is enclosed in a cylindrical container of radius r fitted with a light cork on its top The coefficient of friction between the cork and the container wall is u Initially the gas inside the container is at atmosphere pressure Po Now gas inside the container is slowly heated the cork is pushed out when the temperature of gas becomes four times as it was initially Find the normal force per unit length in kilo newton meter exerted by the cork on the wall of the container Given Po 1 01 105 N m r 40 cm 0 5 cork

A block of mass m 2kg is moving with velocity Vo towards a massless unstretch spring of force constant K 10 N m on a rough surface as shown Coefficient of friction between the block and the ground is 1 2 Find the maximum value of vo so that after compressing the spring the block does not return back but stops there permanently m 1m Forrrrr Rough

Students I II and III perform an exp measuring the acceleration due to gravity g using a simple pendulum They use different lengths of the pendulum and or record time for different number of oscillations The observations are shown in the table Least count for length 0 1 cm Least count for time 0 1 s Student And I II III Ag g Length of the pendulum cm 100 64 0 64 0 20 0 No of oscillations n a E 0 c E E II 8 4 4 Total time for n oscillations 128 0 64 0 36 0 on If E and E and E are the percentage errors in g i e III Time period s 16 0 16 0 9 0 for students I II and III respectively b E is minimum d E is maximum II

Figure shows the magnetic hysteresis loop that is the B H curve for ferromagnetic materials Mark the INCORRECT statement 1 The value of B at H 0 is called remanence 2 The value of H at c is called coercivity 3 A permanent magnet has low remanence and low coercivity 4 An electromagnet has low remanence and low coercivity

the block towards left and is then released If the collision between the block and the wall is completely elastic then the time period of oscillations of the block will be a 2 m b mmmm m V b b 2 c m TU a wall m 0 d TU m 6 k

2 Three consecutive flash photographs of travelling wave on a string are reproduced in the figure here The following observations are made Which of the following options is correct Mass per unit length of the string 6 g cm 0 5 m t 0 t 0 1 s b t 0 2 s Na ical 4 1 Displacement amplitude of the wave is 0 25 m wavelength is 1 m wave speed is 2 5 m s and the frequency of the driving force is 0 2 s 2 Displacement amplitude of the wave is 2 0 m wavelength is 2 m wave speed is 0 4 m s and the frequency of the driving force is 0 7 s 3 Displacement amplitude of the wave is 0 25 m wavelength is 2 m wave speed is 5 m s and the frequency of the driving force is 2 5 s 4 Displacement amplitude of the wave is 0 5 m wavelength is 2 m wave speed is 2 5 m s

91 One end of a long metallic wire of length L is tied to the ceiling The other end is tied to massless spring of spring constant k A mass m hangs freely from the free end of the spring The area of cross section and Young s modulus of the wire are A and Y respectively If the mass is slightly pulled down and released it will oscillate with a time period Tequal to b 2 a 2 m V k c 2 m YA kL Ak d 2 m YA kL YAK n t Buss NAUD m Y kL YAK B sin three identical

The particle executing simple harmonic motion has a kinetic energy K cos ot The maximum values of the potential energy and the total energy ar 2 2 0 and 2K 4 K and 2K respectively 1 K and K Ko 3 and K

5 a What is the difference between rotational motion and simple harmonic motion Can you deduce the expression for the velocity of a particle executing simple harmonic motion What is the condition of getting maximum speed for a simple harmonic oscillator

In the figure the ball A is released from rest when the spring is at its natural length For the block B of mass M to leave contact with the ground at same stage the minimum mass of A must be w M m M A 2M B M C D A function of M and the force constant of the spring

The time period of a particle executing S H M is 8s 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 A B C D 1 2 1 2 1 2 2 1 My Answer Correct Answer

A pendulum of length 10 cm is hanged by a wall making an angle 3 with vertical It is swung to position B Time period of pendulum will be A B C 2 15 s k 6 subsequent motion will not ha OB Correct Answer

Two masses m and m2 are suspended together by a massless sring of spring constant k Fig When the masses are in equilibrium m is removed without disturbing the system Find the angular frequency of oscillation of m v d v m m

If the same weight is suspended from three springs having spring length in the ratio 1 3 5 the period of oscillations shall be in the ratio of A B C 1 3 5 1 3 5 15 5 3 Correct Answer

One end of a spring of force constant k is fixed to a vertical wall and the other to body of mass m resting on a smooth horizontal surface There is another wall at a distance xo from the body The spring is then compressed by 2x0 and released The time taken to strike the wall first time is A B m 6V K m 3 B La m 2x

There is a pendulum executing simple harmonic motion and its maximum kinetic energy is K If the length of the pendulum is doubled and it performs simple harmonic motion with the same angular amplitude as in the first case its maximum kinetic energy is K Relation between them is A B C K2 K 2K K K K Correct Answer My Answer

A The position of a particle moving along x axis is given by x xo cos wt Its speed when it is at mean position is 2x000 Xoto xow 2 00

A particle of mass m is attached to a spring of spring constant k and has a natural angular frequency An external force F t proportional to cos oot ww is applied to the oscillator The time displacement of the oscillator will be proportional to AIEEE 2004 1 m 2 03 0 2 1 m w w 3 1 m w w 4 m w w 2

2x0 1 g attached to a spring of spring is lying on a frictionless floor as constant 100 Nm The block is moved to compress the spring 1 10 cm and then released If the collisions with the shown elastic then the time period of the 90 A ble by wall in front are motion is k 100 Nm 1 moooooo Floan b 01s 100 g 5 cm 015 shog 94 313 25 T5 24 81 3 0132

The position of a particle moving along x axis is given by x xo cos2 wt Its speed when it is at mean position is A B C D 2x0w xow Xow 1 xow Q

4 0 5 s 2 0 75 s 3 0 125 s 4 0 25 s A point mass oscillates along the x axis according to the law x x cos oot r 4 If the acceleration of the particle is written as a A cos cot 8 then AIEEE 2007 19A x 8 1 4 QA xw 6 1 4 2 A x w 8 4 4 A x w 8 3 4 af force constants k and k are connected to a mass m as shown The frequency of oscillation of mass JAIFFE 2007

The x t graph of a particle undergoing simple harmonic motion is shown below The acceleration of the particle at t 2 3 2 cm 2 cm 32 2 cm 32 s 3 cm 32 2 x cm O 12 t s 213 3

A particle is vibrating in simple harmonic motion with amplitude of 4 of 4 cm The displacement of the particle when kinetic energy becomes half of total energy is B C D 10 cm 2 cm 2 cm 2 2 cm

3 In the arrangement shown in the fig the the spring and the thread are ideal The spring is stretched and the two blocks are in contact with a horizontal platform P When the platform is gradually moved up by 2 cm the tension in the string becomes zero If the platform is gradually moved down by 2 cm from its original position one of the blocks lose contact with the platform Given M 4 kg m 2 kg a Find the force constant k of the spring b If the platform continues to move down after one of the blocks loses contact will the other block also lose contact Assume that the platform moves very slowly

Q 24 75 A simple pendulum with a bob of mass 100 g has time period 4 s If the bob is given charge 0 001 C and a vertically upward electric field of magnitude 360 V m is switched on the time period in seconds of the pendulum becomes g 10 m s

A radioactive source is a mixture of two radioactive materials X and Y with mean life time of 6 days and 9days respectively Initially 20 of radiations came from the radioactive decay of X and remaining from Y The time in past at which 80 of radiations came from the decay of X is n ln 2 days What is the value of n

17 A simple pendulum performs simple harmonic motion about x 0 with an amplitude a and time w 4 a period T The speed of the pendulum at x 2 Tibe osinot beli do a 3 A wiss not 2 band 4 w AIPMT Prelims 2009 134 2 3 a T will a 3 2T 0 J a wojs 2

lar motion of a picle The radius of the circle period sense of revolun and the initial position are inated on the figure The simplermonic motion of the x projeon of the radius vector of the ating particle P islamit 308 Colombi Tt a x t sin c x t sin RIO 2 P t 0 B b x t B cos T 30 s NCERT Exemplar 1 d x t B cos t 15 nt 15 BIN x 2

equilibrium The mass of the container The system shown in figure is in the container is p and the volume of with liquid is M density of liquid in displaced downwards through a the block is V If the container is now distance Xo and released such that the block remains well inside the liquid then during subsequent motion a time period of SHM of the container will be 2 b time period of SHM of the container c will be 2n V k Jum amplitude of SHM of the container is 2x0 wwwwww M k

A pendulum bob of mass 8 mg carries an electric charge of 39 2 10 10 C in a horizontal electric field of 20 x 103 NC 1 and is at rest The angle made by pendulum with vertical is nearly O 37 45 O 60 O 30

A man measures the period of simple pendulum inside a stationary lift and finds it T second Now the lift accelerates upwards and the time period is T The acceleration of the lift is 02g 03g O 3 5 g 4 2 g

2 Frequency of oscillation of a body is 6 Hz when force F is applied and 8 Hz when F is applied If both JAIPMT 2004 forces F F are applied together then find out the frequency of oscillation 2

Two point sources separated by 2 0 m are radiating in phase with 0 50 m A detector moves in a circular path around two sources in a plane containing them How many maxima are detected S 2 mi n d ZAD

37 A particle is in linear SHM of amplitude A and time period T If v refers to its average speed during any interval of T 3 then the maximum possible value of vis XIT 3 3 3 A T T 2 3 T a c A A b d 3A T

having surface charge density o is placed in Y Z plane A simple pendulum having bob of mass m and charge q is hanged right to the plate as shown in figure Find out the time period of SHM of the pendulum g acceleration due to gravity m q

A particle is executing SHM along the x axis with amplitude A and time period T At any instant particle is at its left extreme position Time taken by this 3A particle to travel a distance of from the given 2 instance is x 3T 8 3T 2 T 7 4 ET