Simple harmonic motion Questions and Answers

18 A thin uniform rod of mass M 0 112 kg and length L 0 096 m is suspended by a wire that passes through its center and is perpendicular to its length The wire is twisted and the rod set oscillating The period is found to be 2 14 sec When a flat body in the shape of an equilateral triangle is suspended similarly through its center of mass the period is found to be 5 83 sec Find the rotational inertia of the triangle about this axis

4 If x v and a are displacement velocity and the acceleration respectively of a particle executing SHM of fixed time period T then which of the following remains constant with time 1 a T 3 T 2nv eraf 2 4 aT X aT LTD 2 LT 37

A bob of a simple pendulum executing SHM in air has time period To and in water has time period T If density of bob is 4 3 103 kg m then correct relation between T and To is Neglect friction 0 4 T T 3 T 2T T 2 T 2 4 T 4T

5 A particle of mass m is executing oscillation about the origin on the x axis Its potential energy is U x Klx13 where K is a positive constant If the amplitude of oscillations is a then its time period Tis 1 Droportional to a 3 2 Proportional to a 2 Proportional to

A block of mass m compresses a spring of spring constant k through a distance 17 123 as shown in figure The block is not fixed to the spring The period of motion n Find n m of the block is k m 6247 ci Yc ych An Audig k yg ami a hea 21 ych fa chi Bada Tuch of Mi Elastic Wall Rear 1 2 Aa A zefy HJwz 2 na 38 13 1 k moooo m k n In

A wooden cube density of wood d of side e floats in a liquid of density p with its upper and lower surfaces horizontal If the cube is pushed slightly down and released it performs simple harmonic motion of period T ld 1 2 3 2 4 2 p d g ld pg 2 2 lp dg lp V p d g

A uniform horizontal electric field E is established in the space between two large vertical parallel plates A small conducting sphere of mass m is suspended in the field from a string of lengt L If the sphere is given charge q then te period of oscillation of the pendulum is B 2T A 2 L g C 0 2 L Vg qE m 2 g 2 L qE m 2 L Vg qE m

In the figure shown a block of mis attached to a light spring of force constant K and an identical spring hangs from ceiling initially lower spring is in compressed state with 3mg compression equal to When block is k released it strikes upper spring and sticks to it What is the amplitude of oscillation in cm after sticking Given mg 20 N K 100 7 N m Terfy fa m yg ych s da Audich K Ich sch c a fu ja ar huga M va ach 3 3 42 4 7 A d A a 392 2 Mag 4 437 gia ad ug Tu Auch a 1 100 7 N m 20 N K mg k reelle reelle k k 3mg k Equilibrium NCRET RR mg

PLS PROVIDE SEPWISE SOLUTION Show clear diagram marking all the Forces 24 A simple pendulum is attached to a block which slides without friction down an inclined plane ABC having an angle of inclination a as shown A C B While the block is sliding down the pendulum oscillates in such a way that at its mean position the direction of the string is A at angle a to the perpendicular to the inclined plane AC B parallel to the inclined plane AC C vertically downwards D perpendicular to the inclined plane AC

A particle of mass m is released from rest and 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 set of b c X t d 4x t 4 x t A 4x t V x 4 2011

A disc of radius R pivoted at point 0 oscillates in the plane of paper as shown in figure The distance of point O from centre of mass of disc is x Ruch achdi O far uz hacha 3 A Aa tey ggur h da da se za 21 A fare B A 2 2gx x R C D Xic R Time period of oscillations of disc is R 2x Correct Answer R G J 1 2 1 Correct Answer 2 time period is minimum 2 R 2x 2gx 2 Correct Answer The minimum time period is 2 2R 9 The minimum time period is 27 2R g R

In damped oscillations the amplitude of oscillations is reduced to one third of its initial value ao at the end of 100 oscillations When the oscillator completes 200 oscillations its amplitude must be Question Type Single Correct Type 1 2 a0 2 a0 4

The time period of oscillation of the system 11m shown in the figure is given by T nk Find the value of n T ABRI 2k 2 reeeee eeeee m eeeee k Au m 11m nk 2

About its vertical axis a smooth horizontal circular table is given an angular speed A groove is made on the surface along a radius A particle is gently placed inside the grove at a distance from the centre The speed of a 2 the particle w rt table when its distance from the centre is x is Ow a O O 25 1 0 2

4 Which one of the following statements is true for the speed and the acceleration a of a particle executing simple harmonic motion A Value of a is zero whatever may be the value of v B When u is zero a is zero C When u is maximum a is zero D When v is maximum a is maximum ICR SE 2004

a About its vertical axis a smooth horizontal circular table is given an angular speed w A groove is made on the surface along a radius A particle is gently placed inside the grove at a distance from the centre The speed of the particle w r t table when its distance from the centre is x is 2 O w 1 a O w1 72 01 a O w x

A tray of mass M 10 kg is supported on two identical springs When tray is pressed a little and released it executes SHM of period of 2 s When block mis placed on tray period of oscillation becomes 3 s The value of mis m K elleeee 6 5 kg 7 5 kg 12 5 kg 4 5 kg eeeeeee K Tray m 10 kg

Two springs each of unstretched length 20 cm but having different spring constants K 1000 N m and K 3000 N m are attached to two opposite faces of a block of mass m 100 g kept on a smooth horizontal surface as shown in the figure The outer ends of the two springs are now attached to two pins P P whose locations are fixed to the walls as shown in the figure as a result of this the block acquires a new equilibrium position The block has been displaced by small amount from its equilibrium position and released to perform simple harmonic motion then motion is RAM f 100 motion is sec P A new equilibrium position is at 35 cm from P and time period of simple harmonic sec 10 sec 26 20 K od m foooooo VATH plc B new equilibrium position is at 20 cm from P and time period of simple harmonic f 100 C new equilibrium position is at 35 cm from P and time period of simple harmonic motion is P2 D new equilibrium position is at 30 cm from P and time period of simple harmonic motion is see NARAYANA GROUP f 26

A block of mass 1 kg is fastened to a spring The spring has spring constant of 100 Nm1 The block is pulled to a distance of 10 cm from equilibrium position x 0 t 0 and released The kinetic energy of the block when it is at 5 cm away from mean position is 125 mJ 155 mJ 375 mJ 325 mJ

The time period of a particle executing SHM with amplitude A is T What is the minimum time taken by the particle to move a distance A 1 3 T 2 6 T Ta 4

A large simple pendulum of length equal to radius of the earth is making simple harmonic oscillations near the surface of the earth Its time period of oscillation will be approximately 1 30 minute 2 45 minute 3 One hour

Equation of a travelling wave on a stretched string of linear density 5 g m is y 0 03 sin 450t 9x where distance and time are measured in SI units The tension in the string is n N Then find the value of 2n O 25 50 12 5 20

46 A simple pendulum of length L has a bob of mass m The bob is connected to light horizontal spring of force constant k The spring is relaxed when the pendulum is vertical see fig i a The bob is pulled slightly and released Find the time period of small oscillations Assume that the spring remains horizontal b The spring is replaced with an elastic cord of force constant k The cord is relaxed when the pendulum is vertical see fig ii The bob is pulled slightly and released Find the time period of oscillations oncept

A pendulum is oscillating with frequency n on the surface of earth If it is taken to depth below the surface of earth where R is radius of earth New frequency of R oscillations at depth A B n n l

A simple pendulum of length Li from a point object of mass m by a massless string attaches to a fixed pivot point A small peg is place a distance 2L 3 directly below the fixe pivot point so that the pendulum would swing as shown in the figure below Th mass is displaced 5 degrees from the vertical and released How long does i take to return to its starting position fixed pivot point constructed suspended L 1 3 A 3 1 1 3 small peg point object of mass m 2 2 2 g L 1 1 g 3 4 T

17 A collar of spring constant 500 Nm 1 If collar is displaced from equilibrium position by a distance of 2 cm and released what is frequency of oscillation p Collar k mor rooo k NCERT Pg 348 1 5 4 Hz 2 1 78 Hz 3 9 36 Hz 4 3 26 Hz 18 Two identical springs of spring constant K each are attached to block of mass m and fixed supports as shown in figure a The period of oscillation was observed to be T If one more identical spring is attached as shown in figure b then new period will be NCERT Pg 345 m 4 kg k k moon m mom Fig a m k 1 3 T 19 19 2 3 27 4 x T A particle exe energy which potential energ assumed to be versus position 1 SA A 2 A 0

How to check that particle starts from extreme position A block of mass 2 kg is attached to a spring of spring constant 50 N m 1 The block is pulled a distance of 5 cm from its equilibrium position at x 0 on horizontal frictionless surface and then released The displacement of block at any time t is x 0 05 cos 5t m x 0 05 sin 10t m Xx 0 05 sin 5t m

A simple pendulum of length L is suspended from a roof of a trolley A trolley moves in horizontal direction with an acceleration a What would be the period of oscillation of a simple pendulum g is acceleration due to gravity A2 TVL a g B C 2 a g 2 5 D 2 TT 20 L g a

A pendulum has length of 0 4 m and maximum speed 4 m s When the length makes an angle 30 with the horizontal its speed will be sin cos 0 5 and g 10m s A2 2 m s B 3 m s c2 5 m s D2 3 m s

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 S H M of period T If the mass is increased by m the time period becomes What is the ratio 25 9 A B C 16 al 25

simple Starting from the mean position a body oscillates harmonically with a period of 2s Its kinetic energy will become 75 of the total energy after Question Type Single Correct Type 1 2 3 1 6 11 12 1 13 H sec 1 sec sec sec

The system shown is hanging in equilibrium well above the ground When the string is cut the time taken by the spring to reach its natural length can be Take n 10 A s B s C s 60kg F 1800N m 30kg ceeeeee

Board Competitive Exams Level 1 to 10 Find the ratio of the extension in upper spring to lower spring m k 1 m K K Feeeeeeee K m k 2 m k m m k

space at points L 0 and L 0 Another particle with mass m and charge q is placed at the origin Now this particle is displaced by a distance of y along the y axis and then released Show that this particle will execute oscillatory motion Solution BOARDS The only way to prove the particle executes oscillatory motion is to prove that the particle executes SHM because oscillatory motion is a consequence of SHM Now if we are able to prove that the force on the particle of charge q is restoring and is proportional to the displacement then it will be enough to conclude that the charged particle executes SHM Suppose the particle of charge q is displaced along the y axis by a distance of y as shown in the figure F 2F cos 0 net Q L 0 Q L 0 F 9 00 0 y Q q L 0 F Q L 0 X If the force on q by Q is given by F then the net force on the charge q by both the charges is given by

Choose incorrect statement regarding oscillation 1 The potential energy of a body executing SHM at mean position can be non zero 2 The total energy of oscillating body remains constant at all value of x and t 3 The time period of a spring pendulum in falling freely lift is infinity 4 The effective length of seconds pendulum is about 1 metre

A pendulum clock and a wrist watch both are taken deep in a mine Which of the following statements is correct 1 Both will show correct and same time 2 Pendulum cock will run fast and wrist watch will run slow 3 Pendulum cock will run slow and wrist watch will give correct time 4 Both will run slow and give same time

1 600 cal 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 simple harmonic oscillations with a time period T If the mass is increased by m then the time period increased by 10 The ratio of m M is 25 21 4 1 100 16 17 2 30 50 3 rer medium with a loss of 36 of the

A U tube of uniform bore is placed with its arm vertical The total length of liquid in two arms of tub is L The time period of oscillation of liquid columr when it is displaced is 12 1 T 2T 3 T 2T 2L 2 T 2n 4 T 2 L 2g L

A simple pendulum of length L has mass M and it oscillates freely with amplitu A At extreme position its potential energy is g acceleration due to gravity A B2 MgA L C MgA 2L D MgA L MgA

A spring produces extension x by applying a force F N A body of mass m suspended from spring oscillates vertically with a period T The mass of the suspended body is neglect mass of spring A B C D 2T F x T F 4 x T F x T F

The length of the seconds pendulum is 1 m on the earth If the mass and diameter of the planet is half that of the earth then the length of the seconds pendulum on the planet will be A 0 5 m B C 1m 1 5 m

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 of oscillation now will be A B C T 2 T T 2

Question No 18 If y 5 mm sint is equation of oscillation of source S and y 5 mm sin t be that of S Si Options and it takes 1 sec and 12 sec for the transverse waves to reach point A from sources S and S respectively then the resulting amplitude at point A is A 5 2 3 mm S 6

A central force with potential r km k 0 is acting on a particle Calculate the angular frequency if the particle moving in a circle whose radius answer a 2 b 2ka c SASARA d

3 A particle is executing SHM with a period of T seconds and amplitude A meter The shortest time A it takes to reach a point at seconds is 1 T 4 2 T 6 from A 2 8 in

An insect trapped in a circular groove of radius 17 12 cm moves along the groove steadily and completes 7 revolutions in 100 s The linear speed of the insect is 1 4 3 cm s 3 6 3 cm s 2 5 3 cm s 4 7 3 cm s 12 fren and face 1007 af refra fat 1 4 3 cm s 3 6 3 cm s 2 5 3 cm s 4 7 3 cm s

a 0 Two particles are oscillating along two close parallel straight lines side by side with the same frequency and amplitudes They pass each other moving in opposite directions when their displacement is half of the amplitude The meanpositions of the two particles lle on a straight line perpendicular to the paths of the two particles The phase difference is a b 0 T 6 2 c 3 d n tical piano wires kept under the same tension T

A mass M is hung from a lower e nd of a light spring attached to ce iling If the mass is allowed to fal l from normal length of spring th e maximum extension in spring i s x0 Now this mass is set for osci llations in vertical direction the p eriod of oscillation will be

A set of 25 tuning forks is arranged in a series of decreasing frequencies Each fork produces 3 beats per econd when sounded with succeeding fork If the first fork frequency is double the last the frequency A of the first fork is 144 Hz B of the third fork is 135 Hz C of the fifteenth fork is 102 Hz D of the last fork is 69 Hz

A free spring hangs from a support and has a length of 20 cm Attaching a mass M to the spring causes it to oscillate If the mass is attached to the free spring and then released from rest the lowest position of the oscillation is 10 cm below the free spring length a Where is the equilibrium position b What is the frequency of oscillations ans 2 2 cycles sec c What is the velocity when the mass is 5 cm below the free spring length ans 70 cm sec d A second mass of 300 gm is added to the 1st mass When this system oscillates it has half the frequency of the system with mass M alone What is the mass M ans 100 gm e Where is the new equilibrium position ans 15 cm below the old position