Simple harmonic motion Questions and Answers

A mass M attached to an horizontal spring executes SHM with a amplitude A When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with A amplitude A2 The ratio of A YOU B M m M C M M m D MM 2 M m M 1 2 is

A block P of mass m is placed on a frictionless horizontal surface Another block Q of same mass is kept on P and connected to the wall with the help of a spring of spring constant k as shown in the figure s is the coefficient of friction between P and Q The blocks move together performing SHM of amplitude A The maximum value of the friction force between P and Q is 1 KA mmmmmm Smooth surface Q P

Option 4 Skip Question 22 Question A spring of spring constant k is cut into three parts of lengths in ratio 1 2 1 The algebraic addition of spring constants of these springs will be 21 10k

The displacement of a particle is given at time t by x A sin 2wt B sin wt Then A B The motion of the particle is SHM with an amplitude of C C The motion of the particle is oscillatory with a time period of T A V The motion of the particle is not SHM but oscillatory with a time period of T w The motion the porti lo in o pori B 4 2w

A spring block system is fixed in a train suddenly train starts moving with constant acceleration ao Taking origin at initial position of block what is equation of motion for block in reference frame of train Force constant of spring is k Neglect friction between block and train mmmmmmmm mao mao k k mao k COS k Om ma cost mao k k mao k a COS Ft

to two identical springs as shown in figure The extension in upper spring is twice the compression in lower spring Then Clear Response upper spring is cut just after that the block will accelerate upward with 2g 3 If upper spring is cut just after that the block will accelerate downward with 2g 3 If lower spring is cut just after that the block will accelerate upward with g 3 If lower spring is cut just after that the block will appolorato de with 10

50 A bob of a simple pendulum has mass m and is oscillating with an amplitude a if the length of the pendulum is L then the maximum tension in the string is cos 0 1 g acceleration due to gravity a Amg 1 7 B mg 1 C mg 1 D mg 1 a

A body performs linear simple harmonic motion of amplitude A At what displacement from the mean position the potential energy of the body is one fourth of its total energy A B C D AIM AN 3 2 3A 4 A

A spring executes S H M with mass 10 kg attached to it The force constant of the spring is 10 N m If at any instant its velocity is 40 cm s the displacement at that instant is Amplitude of S H M 0 5 m 0 3 m 0 2 m A B C D 0 4 m 0 45 m

A small mass m is suspended at the end of a wire having negligible mass length L and cross sectional area A The frequency of oscillation for the S H M along the vertical line is Y Young s modulus of the wire A B C YA 2 mL 2 YA mL YA 2 mL 1 2 2 T YA D 2 mL

A particle performs S H M with amplitude A Its speed is tripled at the instant 2A when it is at a distance of from the mean position The new amplitude of the motion is A B C D 5 m Sm S m 5A 3 7A 3 2A 3 A

82 A body executes S H M under the action of force F with time period T If the force is changed to F2 it executes S H M with period T If both the forces F and F2 act simultaneously in the same direction on the body its time period is

18 A particle is executing SHM according to the equation x A cos oot Average speed of the particle during the interval 031 T 600 1 3 3 A00 2 3400 I 2 3 A00 4 3400 2 3 TT

6 The bob of a simple pendulum executes SHM in water with a period t while the period of oscillation of the bob is to in air Neglecting the frictional force of water and given that the density of the bob is 4 3 x 1000 kg m What relationship between t and to is true 3 1 t to 2 t 4to 3 t 2to 4 t 1 2

Graph of displacement x time t for a particle executing SHM is shown below The corresponding acceleration a versus time t graph will be tr 0 A W AA A CTS

ork done in accelerating it from rest to v 25 A block of 200 g mass is dropped from a height of 2 m on to a spring and compress the spring to a distance of 50 cm The force constant of the spring is Kerala CET 2013 a 20 Nm c 30 Nm b 40 Nm 1 d 60 Nm 1

The radius of the circle the periodic revoluti sense of revolution are indicated in given figure Obtain the simple harmonic motion of the x projection of the radius vector of the revolving particle P AP t 0 O x 4sin 4 m x 4 cos O x 4 sin Ox 4cos T 6s

A uniform plank of mass m 2 kg free to move in the horizontal direction only is placed at the top of a solid cylinder of mass M 2 kg and radius R The plank is attached to a fixed wall by means of a light spring of spring constant K 11 N m There is no slipping between the cylinder and the plank and between the cylinder and the ground Find the angular frequency rad s of small oscillation of the system fay z yg agxu aed c 2 kg ch a 2f8 92 zu Gala ch K 11 N km Audig A gch ar g a ku ja aa au ac aa am uuda h qw c s Muda 15 31 Agu 3 4 a ufu AA m R 2 kg R over vervo K

3 E 8i NC 4 81 NC 3 A particle is executing a simple harmonic motion Its maximum acceleration is ct and maximum velocity is B Then its time period of vibration will be 4 2mB 3 4 B A ray of light passes through equilateral prism 33 34 3 E 81 NC 1 4 E 81 NC en af d 2n a 812 1 5 3ales and was gre

A simple pendulum is suspended from the ceiling of a vehicle its time period is T Vehicle is moving with constant velocity then time period of simple pendulum will be 1 Less than T 2 Equal to T 3 More than T 4 Cannot predict

11 A simple pendulum has a length I and the mass of the bob is m The bob is given a charge of q coulomb The pendulum is suspended between the vertical plates of a charged parallel plate capacitor If E is the electric field strength between the plates the time period of the pendulum is given by a 2 b 2 1 9 9 1 9 98 c 2 773 d 2n 112

The amplitude of the vibrating particle due to 38 superposition of two SHMs y sin t and y sin oot is 1 1 2 2 3 3 4 2 en y sin ot 7 a Y sin tre 1 1 2 2 3 3 4 2

A particle is in linear simple harmonic motion between two points A and B 10 c apart Take the direction from A to B as the positive direction and give the signs velocity acceleration and force on the particle when it is a at the end A b at the end B c d e f at the mid point of AB going towards A at 2 cm away from B going towards A at 3 cm away from A going towards B and at 4 cm away from B going towards A

uniform cylinder with mass m and radius R is connected to a spring with spring constant k as shown in the Fig A horizontal board with mass m res nder and the board also rests on top of a frictionless support near its left end The system is slightly displaced from equilibrium There is no slip cylinder and the board or between the cylinder and the ground The angular frequency of the oscillatory motion is p The value of frictionless m keeeeee 11p m is k

slipping on the hemisphere Two identical particles A and B each of mass M are fixed on the two 20 ends of a uniform rigid rod of length m and same mass M The 7 upper mass A is restricted to move on a smooth horizontal rail and the rod is free to swing along the rail Take g 10 m s Find the angular frequency of oscillation in rad s of the system if it is displaced slightly from its equilibrium position and released 00 B A

Q1 a A block having a mass of 0 8 kg is suspended from a spring having a stiffness of 120 N m If a dashpot provides a damping force of 2 5 N when the speed of the block is 0 2m s determine the period of free vibration 5marks

21 a A block having a mass of 0 8 kg is suspended from a spring having a stiffness of 120 N m If a dashpot provides a damping force of 2 5 N when the speed of the block is 0 2m s letermine the period of free vibration 5marks

The potential energy of a simple harmonic oscillator at mean position is 2 joules If its mean K E is 4 joules its total energy will be 1 7 J 2 8 J 3 10 J 4 11 J 4 V or M and M have ec KE 9

In a sinusoidal wave the time required for a particular point to move from maximum displacement to zero displacement is 0 170 s The frequency of wave is a 0 73 Hz b 0 36 Hz c 1 47 Hz d 2 94 Hz 1998

A uniform cylinder of mass 5 kg radius 10cm v and height 30cm is floating in water with its axis vertical If the cylinder is displaced from its equilibrium position It will execute SHM if it is displaced vertically by a small distance It will execute SHM if it is displaced horizontally by a small distance It will execute periodic motion if it is displaced vertically by a small distance None of these A

An oscillating simple pendulum has a small bob of mass m and a metallic thread of length In which of the cases the time period of the pendulum would increase A The temperature increases B The point of suspension is moved vertically downwards with some constant acceleration less than g C The bob is replaced with a bob of larger mass D The bob is positively charged and a uniform electric field is switched on in vertically downward direction

The force on a body executing SHM is 4 N when the displacement from mean position is 2 cm If amplitude of oscillation is 10 cm then the maximum kinetic energy associated with the SHM will be NCERT Pg 351 1 1 J 3 2 J 2 4 J 4 3 J

ALLEN 56 tuning forks are so arranged in series that 22 each fork gives 4 beats per sec with the previous one The frequency of the last fork is 3 times that of the first The frequency of the first fork is 1 110 2 56 3 60 4 52 56 34 or aften for a and aus al SINH RA I SI v zala i 3 T N TR zata nafa 1 110 2 56 3 60 4 52

A diatomic molecule having atoms of masses m and m and its potential energy function about the equilibrium position ro is given by U r A B r ro where A and B are constants When the atoms vibrate at high tem perature the frequency of vibration will be 1 B 1 2B 2 Vm m 2 Vm m A C 1 2 B m m m m2 B D 1 2B m m 2 V m m

A simple pendulum 50 cm long is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration 3g m s The period of small oscillations of the pendulum about its equilibrium position is g m s 3g m s J 1 0 s O 2 S 1 53 s 50 cm

A string is 2 4 m long and the speed of the sound along this string is 450 m s Calculate the frequency of the wave that would produce a third harmonic Assume that the strings has nodes at both ends 1 Point 280 Hz 560 Hz 230 Hz 720 Hz

A spring with a spring constant of 15 0 N m is stretched 8 50 m What is the force that the spring would apply 6 50N 128N 1 76N O 23 5N

What quantity does the distance marked Z represent y Z W 2 A A wavelength O frequency O amplitude X

The original period of a simple pendulum is T The length of the simple pendulum is then quadrupled and its mass is doubled What is the new period of the simple pendulum in terms of T a T b 27 c 47 d 12T

A horizontal spring attached to a wall has a force constant of k 700 N m A block of mass m 1 80 kg is attached to the spring and rests on a frictionless horizontal surface as in the figure below ww m x 0 x x 2 x x a The block is pulled to a position x 5 40 cm from equilibrium and released Find the potential energy stored in the spring when the block is 5 40 cm from equilibrium 3 b Find the speed of the block as it passes through the equilibrium position m s c What is the speed of the block when it is at a position x 2 2 70 cm m s

HINT m Need Help Read It k y 0 When released the block travels across a horizontal surface and up an incline Neglecting friction find the block s maximum height in m if the spring constant is k 565 N m The acceleration of gravity is g 9 80 m s 4 Points DETAILS max m Watch It SERCP11 13 4 OP 018 MY NOTES y 0 a What is the block s maximum speed in m s after it is released m s ASK YOUR TEACHER PRACTICE ANOTHER A 0 50 kg block rests on a frictionless horizontal surface where it is attached to a massless spring whose k value equals 20 5 N m Let x be the displacement where x 0 is the equilibrium position and x 0 when the spring is stretched The block is pushed and the spring compressed until x 4 00 cm It then is released from rest and undergoes simple harmonic motion b How fast is the block moving in m s when the spring is momentarily compressed by 2 40 cm that is when x 2 40 cm m s c How fast is the block moving in m s whenever the spring is extended by 2 40 cm that is when passing through x 2 40 cm m s

4 A 0 065 kg object is attached to a spring with a spring constant of 100 0 N m The other end of the spring is attached to a wall in such a way that it rests on a frictionless horizontal surface A force is exerted on the spring so that it experiences simple harmonic motion A 6 a How much work would be done on the spring to compress it by 11 0 cm b Assuming that there is no friction describe the energy conversions that take place being sure to explain the location of maximum elastic potential energy and maximum kinetic energy c What will the speed of the object be when it is passing the point of being compressed by only 5 5 cm Assume that the mass of the spring is negligible

In the arrangement of a spring block system the pulleys and the springs are massless An inextensible string passes over the pulleys and a mass m hangs from it The period of small vertical oscillations of the mass under xm 2 TH Find the value of x K M cic Aciu z ga fazA ay Gwgada 31 yg d zz AzAu 342 guza am 5w47 m ga ach 1 gua fer gravity is T A T 2 Jimm K xm K B m A AA

A spring balance has a scale that reads from 0 to 60 kg The length of the scale is 30 cm A body suspended from this balance and when displaced and released oscillates with a period of 0 8 s what is the weight in N of the body when oscillating

An elastic spring of force constant k and 20 natural length 3 l is cut into two parts so that their natural lengths are 200 and lo respectively One end of these springs are attached to points P and Q on a fixed vertical wall and tied with a block of mass m A B C D 0 0 0 0 0 0 m m In equilibrium the distance of block from the vertical wall is 400 3 In equilibrium the distance of block from the vertical wall is 500 3 The force constant of shorter part of the spring is 3k The force constant of larger part of the spring is 2k 3

A mass m 1 0 kg is put on a flat pan attached to a vertical spring fixed on the ground The mass of the spring and the pan is negligible When pressed slightly and released the mass executes simple harmonic motion The spring constant is 500 N m What is the amplitude A of the motion so that the mass m tends to get detached from the pan take g 10 m s The spring is stiff enough so that it does not get distorted during the motion A A 2 0 cm B A 2 0 cm CA 2 0 cm 10 500 2 n k D A 1 5 cm 3 ff k 201

Q 97 the force on the first piston A particle executes simple harmonic motion Q 97 with a period of T second and amplitude A metre The shortest time it takes to reach point metre from its mean position in seconds is 1 T 3 T 8 2 T 4 4 T 16 1 T 3 T 8 for fenf A 2 T 4 4 T 16 HO GRI fa a

Find maximum distance between two particles in SHM along two parallel close line with same meanposition and frequency and amptitude A It is found that at some instant the displacement velocity of particles are same in magnitude but opposite in direction A 2 3 A 1 3 4 2A 3 A

The radius of the circle the periodic revolution the initial position and sense of revolution are indicated in given figure Obtain the simple harmonic motion of the x projection of the radius vector of the revolving particle P P t 0 3 x 4 sin 4 m 2 T 6s 1 x 4sin 1 x 2 x 4cos 3 t n X 3 4 x 4cos t T 2 3 t r

Q 114 A particle moves so that its position vector is given by 7 cos cotx sin coty Where to is a constant Which of the the following is true 1 Velocity and acceleration both are perpendicular to i 2 Velocity and acceleration both are parallel to i 3 Velocity is perpendicular to and acceleration is directed towards the origin 4 Velocity is perpendicular to and accelertaion is directed away from the origin Q 114 fe fer cos cotx sin coty are far ren 8 Gretas frentas 1 f 1 2 3 Panga site fer directed 1 4 ang Tafsire fre 1