Simple harmonic motion Questions and Answers

Code A 29 The equation of a transverse wave propagating in a string is given by y 0 04 sin x 40f where x and y are in metre and t is in second If linear density of the string is 5 x 104 kg m then the tension in the string is 1 0 08 N 3 8 N 2 0 8 N 4 800 N

A light inextensible string wound over a cylindrical fixed horizontal steel rod as shown Coefficient of friction between rod and string is 7 Two blocks of masses m and m are connected to two ends of string as shown Number of turns of string on the rod can be counted from the figure The ratio such that my starts moving up is e where N m

A block is attached to a spring of spring constant k initially in natural length A constant force F starts acting on a block as shown in figure All surfaces are frictionless F k mmmmmm 2 ix 0 Question Type Multiple Correct Type Potential energy function for this combination of forces can be U x kx FX F 2k X Potential energy function for this combination of forces can be F U x kx Fx F

A block of mass m placed on a frictionless horizontal floor is connected with two identical springs each of force constant k One end of the left spring is connected to a fixed support and one end of the right spring is free Initially the block is at rest the springs are collinear and relaxed If someone begins to pull the free end of the right spring with a constant velocity u away from the wall how far will the block move before it acquires a speed equal to u

A sound wave of 40 cm wavelength enters the tube as shown What must be the smallest radius r such that a minimum will be produced at the detector Source 1 15 5 cm 3 17 5 cm 2 16 5 cm 4 18 5 cm Detector

Three identical elastic cords each of force constant k and almost zero relaxed lengths are connected at their one end to a particle of mass m and the other ends of the cords are connected to three equally spaced points A B and C on a rigid ring placed on a frictionless tabletop Mass of the ring is n 2 times the mass of the particle In equilibrium the system stays at rest with the particle at the centre of the ring Now the ring is held and the particle is pulled horizontally to a point P at a distance ro from the centre O of the ring and then both of them set free simultaneously a Find period of the oscillatory motion b Assume initial location of the centre of the ring as origin and the line OP as the x axis express position of particle x and centre of the ring no funct of tir B

commcom 7 Two identical small discs each of mass m placed on a frictionless horizontal floor are connected with the help of a spring of force constant k The discs are also connected with two light rods each of length that are pivoted to a nail driven into the floor as shown in the figure by a top view If period of small oscillations of the system is 2 mik find relaxed length of the spring

A particle undergoes SHM with frequency 0 68 Hz At t 0 it has displacement xo 4 cm and velocity Vo 19 5 cm s Determine the amplitude of this motion The amplitude A Units Select an answer

3 P P P P 4 P P P P 7 If a simple harmonic motion is represented by d x dt 1 2 3 Bx 0 its time period is 2n B 2 2 B 2 VB

A square plate of mass M and side length L is hinged at one of its vertex A and is free to rotate about it The plate performs oscillations about a horizontal axis passing through A lying in the plane of nL Find n figure The time period of small oscillations is given by T 2 2g rect Answer 1 16 to 1 17 ur Answer 6 wwwww A

A 16kg mass is attached to a spring having spring constant of 4 N cm The mass is started in motion by stretching the spring 2cm from the equilibrium position and releasing it from rest i e the initial velocity is zero 1 Find the position of the mass as a function of time ii How far from the equilibrium position will the mass be after 10seconds

3 For the system shown in the given figure the moment of inertia of the weight W and the ball about the pivot point is 10 The natural frequency of the system is given by 1 2 Ka Wb lo fn The system will vibrate when W PUBLICAT a b Ka W c b Kg W l K b b Ka W dla 0

The motion of an object with mass 10 kg at the end of a spring is studied Given that damping force 5 N spring constant 4 N external force cos 2t If the object is released from rest at 5 M below of its equilibrium Evaluate the displacement of the object at any time t

The differential equation representing the S H I U particle is 16 d y 2 dt 9y 0 If particle is at mean position initially then time taken by the particle to reach half of its amplitude first time will be NCERT Pg 349 1 4 9 T 2 A 5 9 2 S

mg 66 A simple pendulum has a length 1 mass of bob m The bob is given a charge q coulomb The pendulum is suspended in a uniform horizontal electric field of strength E where E vertically downward having magnitude m mg Fa The time period of 71

A particle of mass m is executing a motion in which the velocity when plotted against displacement follows the curve where a and b are positive constants and a b If U K and T denote the average potential energy average kinetic energy and total energy of the particle respectively then 1 U K 2 T 3 1 6 mb2 42 v 2 a 6 2 1

Frequency of oscillation of a block with two sprin separately are 3Hz and 4Hz Frequency of oscillat of same block with both springs connected in para is 1 7 Hz 3 Hz 12 7 2 5 Hz 4 None of these

A block of mass m attached to a massless spring is performing oscillatory motion of amplitude A on a frictionless horizontal plane If half of the mass of the block breaks off when it is passing through its equilibrium point the amplitude of oscillation for the remaining system become fA The value offis hongmathongo mathongo matlongo 1 maran 2 10 3 math 4 2 mathongo 2

A certain simple harmonic vibrator of mass 100 g has total energy J Its displacement from mean position is 1 cm when it has equal potential and kinetic energies The amplitude A and frequency n of vibration are OA 2 A 7 2 cm n cm n O A 2 cm n 1000 X 500 Hz Hz 500 Hz R 1000 OA 2 cm n Hz R

6 A spring of negligible mass suspended vertically from one end is stretched a distance of 20 cm under gravity when a 5 gm mass is attached to the other end The spring and mass are now placed on a horizontal frictionless table and the no mass end of the spring is fixed at a point The mass is pulled away a distance 20 cm beyond the equilibrium position and released

A block is on a horizontal slab which is moving horizontally and executing S H M The coefficient of static friction between block and slab is u If block is not separated from slab then angular frequency of oscillation will be A Amplitude 1 00 3 00000 VI ug A A 2 4 ug A g

Figure shows two identical cubes each of m connected by a light spring of force constant k The spring is initially compressed and the cubes are connected by a thread with spring compressed Find the initial compression so that on burning the thread finally lower cube will break off from ground 2005

The displacement harmonic motion is given by y Ao Asinot Bcosot Then the amplitude of its oscillation is given by 1 A A B 2 A B 3 A A B 4 A B of a particle executing simple

101 Two independent simple harmonic motions y A TC sin wt and y A sin wt are superimposed 3 on the same particle The resultant simple harmonic motion is 1 y 3A sin ot 2 y 4A sin wt H 3 RC T 60

18 When a particle executing SHM oscillates with a frequency v then the kinetic energy of the particle WB JEE 2014 a changes periodically with a frequency of v changes periodically with a frequency of 2 v c changes periodically with a frequency of v 2 d remains constant

A block of mass m is attached from a spring of spring constant k and dropped from its natural length Find the amplitude of S H M Solution www m

27 A particle executes SHM in accordance with x A sin oot If t is the time taken by it to reach from x 0 to x 3 A 2 and t2 is the time taken 3 2 A to x A the value by it to reach from x MP PMT 2013 of t t is a 2 b 2 e None of the these c 3 d 3 1986

A block of mass m is connected rigidly with a smooth wedge plank by a light spring of stiffness k If the wedge is moved with constant velocity vo then find the work done by the external agent until the maximum compression of the spring mmm 5

A particle oscillating in a field with potential energy is given by V x k x If the amplitude of small oscillation is a then time period T is Proportional a Proportional to va Proportional to a 2

Find the angular frequency w in rad s of mass M when displaced from its equilibrium position and then released for the system shown in figure Consider pulley and string to be ideal Given M 25 kg k 100 N m 1 Inextensible String 2 1 O 1 2 M Question Type Single Correct Type ellele spring with spring constant k Pulley

A wire of length 100 cm and mass 1 25 g is stretched with a tension of 100 N If the wire is set into vibration and touched lightly with a feather at a point one third of its length from one end calculate the frequency of the note emitted O 475 Hz O 500 Hz O 350 Hz O 425 Hz 2 pc

A light insulated rod AB with two small identical metal balls connected to its ends is placed in uniform electric field with its length parallel to electric field Charges on ball are q and q and mass of each ball is m rod length is I Assuming gravity free space if rod is disturbed by angle 0 30 from equilibrium position about centre of the rod and released instantaneous angular acceleration of rod is qE ml 2qE ml 39E ml qE 2ml Asked by 3109459 aesl id Standard XII Stream NEET Aug 1 2021 at 11 57 AM Add your responses Type Text

A metallic rod of length is tied to a string of length 27 and made to rotate with angular speec on a horizontal table with one end of the string fixed the e m f induced across the end of the rod is JEE Main 2013 2Bo 3Bw 2 A B 2 5Bw 2 2 4Bw D

The ends of a stretched wire of length L are fixed at x 0 and x L In one experiment the displacement of the wire is y Asin x L sin wt and energy is E and in E and in another experiment its displacement is y Asin 2 x L sin 2wt and energy is E2 Then Question Type Single Correct Type 1 E E 2 E2 2E 3 E2 4E

3 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 The acceleration of the lift is 2T 3 1 2 g 3 3 5 g 2 3 g 4 4 2 g

A small body of mass m is attached at B to a hoop of mass 3m and radius r The system is released from rest with 0 90 and rolls without sliding then which of the following are correct B A B C 0 Angular acceleration of hoop is initially Net acceleration of hoop is 2 initially Normal reaction just after release in is nearly 3 88mg Frictional after release 0 5mg

A uniform rod of length f lies on a frictionless horizontal surface One end of the rod is attached to a pivot An un stretched spring of length L lies on the surface perpendicular to the rod one end of the spring is attached to the movable end of the rod and the other end is attached to a fixed post When the rod is rotated slightly about the pivot it oscillates at frequency f l Pivot Not to scale Now consider the situation when The spring attachment is moved to the midpoint of the rod and the post is moved so the spring remains unstretched and perpendicular to the rod The system is again set into small oscillations What is the new frequency of oscillation Pivot Post Post le

10 The amplitude and the periodic time of a SHM are 5 cm and 6 s respectively At a distance of 2 5 cm away from the mean position the phase will be JCECE 2012 TC 5t 12 3 b T 4 c 6 d sin

v 8 A copper sphere attached to the bottom of a vertical spring is oscillating with time period 10 s If the copper sphere is immersed in a fluid assume the viscosity of the fluid is negligible of specific gravity of that of the copper then time period of the 10 4 EAMCET 2015 oscillation is a 5 s c 2 5 s 06 d 20 stol 10 s

a k k c k k k k R2 d kqk k k 7 A simple harmonic oscillator consists of a particle of mass m and an ideal spring with spring constant k The particle oscillates with a time period T The or spring is cut into two equal parts If one part oscillates with the same particle the time period will be AIIMS 2012 T T a 2 T b 2 T T 2 of a simple c ML T d 2 T pendulum is kep of oscillati

26 A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all directions The rod is kept in the horizontal position by a vertical inextensible string of length 20 cm fixed at its mid point The bob is displaced slightly perpendicular to the plane of the rod and string The period of small oscillations of the system in the form is sec and value of x is g 10 m s TX 10 l 20 cm

2 3 Two pendulums have time period T and 5T 4 They starts SHM at the same time from the mean position What will be the phase difference between them after the bigger pendulum completed one oscillation UP CPMT 201 d 30 a 45 b 90 c 60 of a particle executing SHM is 4 cm particle is 16 c

1 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 min kg is NEET 2016 9 16 3 4 b 4 3 c 16 9 d

7 A particle of mass 40 g executes a simple harmonic motion of amplitude 2 0 cm If the time period is 0 20 s find the total mechanical energy of the system a 7 9 x 10 J b 8 9 x 10 3 J c 9 9 10 3 J d 6 9 10 3 J

9 55 A mass of 0 2 kg is attached to the lower end of a massless spring of force constant 200 Nm the upper end of which is fixed to a rigid support Which of the following statement is true a In equilibrium the spring will be stretched by 1 cm b If the mass is raised till the spring becomes unstretched and then released it will go down by 2 cm before moving upwards c The frequency of oscillation will be nearly 5 Hz d All of the above

2 Two masses 8 kg and 4 kg are suspended together by a massless spring of spring constant 1000 Nm When the masses are in equilibrium 8 kg is removed without disturbing the system The amplitude of oscillation is a 0 5 m b 0 08 m c 0 4 m d 0 04 m

76 A mass M 5 kg is attached to a spring as shown in the figure and held in position so that the spring remains unstretched The spring constant is 200 Nm The mass M is then released and begins to undergo small oscillations The amplitude of oscillation is T ku 2 2 g WH a 0 5 m 2 m kit Pkn R K x kika wwwwwwwww Hellllll M b 0 25 m d 0 1 m

orm spring whose unstressed length is 1 has a force constant k The spring is cut into two pieces of unstressed lengths 1 and 12 where l nl 2 where n being an integer Now a mass m is made to oscillate with first spring The time period of its oscillation would be a T 2n c T 2n mn Vk n 1 m Vnk b T 2n m Vk n 1 d T 2n m n 1 nk

42 In a spring mass system the length of the spring is L a 4 Hz and it has a mass Mattached to it and oscillates with an angular frequency oo The spring is then cut into two parts one i with relaxed length aL and the other ii with relaxed length 1 a L The force constants of the two springs A and B are k k k k Do b and and 1 a 1 a a a c ak 1 a k M a d k and k sdo raid

C Answer the following questions 1 What happens to the time period of a simple pendulum if i The amplitude is made four times The gravity at a place is increased 2 State and define the SI unit of heat 1