Simple harmonic motion Questions and Answers

5 A particle of mass 2 kg is attached with a spring of 1m it stiffness 72 N m When block is at x moves with maximum speed The block moves with 24 m s while passing through x 4m Find out the x coordinates in m where it s velocity will be zero 1 4 6 2 5 6 3 4 1 4 None of these

27 The particle executing simple harmonic motion has a kinetic energy Kocos wt The maximum values of the potentia energy and the total energy are respectively a Ko 2 and Ko c Ko and Ko b Ko and 2Ko d 0 and 2K

A container of mass m is pulled by a constant force in which a second block of same mass m is placed connected to the wall by a mass less spring of constant k Initially the spring is in its natural length Velocity of the container at the instant when compression in spring is maximum for the first time F 0000000000 111 F RF I

A ring attached with a spring is fitted in a smooth rod The spring is fixed at the outer end of the rod The mass of the ring is 3 kg and spring constant of the spring is 300 N m The ring is given a velocity V towards the outer end of the rod And the rod is set to be rotating with an angular velocity w The ring will move with constant speed with respect to the rod if j j j j j j ring Natural length of spring is same as that of length of rod

A wooden block performing SHM on a frictionless surface with frequency Vo The block carries a charge Q on its surface if now a uniform electric field E is switched on as shown then the SHM of the block will be mmmm Q E 1 of the same frequency and which shifted mean position 2 of the same frequency and with the same mean position 3 of change frequency and with shifted mean position 4 of change frequency and with the same

A particle in S H M is described by the displacement function x t acos t e If the initial t 0 position of the particle is 1 cm and its initial velocity is cm s The angular frequency of the particle is rad s then it s amplitude is 1 cm 2 cm 2 cm 2 5 cm

The light waves from two independen monochromatic light sources are given by y 2 sin wt kx and y 3 cos ot kx then the following statement is correct 1 Both the waves are coherent 2 Both the waves are incoherent 3 Both the waves have different time periods MY Nono of the

If a bob of the simple pendulum having negative charge q is made to oscillate in a uniform electric field acting vertically upward direction then its time period 1 Increases 2 Decreases 3 No effect of the electric field 4 Decreases or increases

A small spherical steel ball is placed a little away from the centre of large concave mirror whose radius of curvature is 2 5 cm When ball is released it begins to oscillate about centre The period of oscillation is g 10 ms 1 3 14 s 2 5 23 s 3 1 21 s 4 4 31 s

2 A particle moving along x axis has its position varying with time given by x 4 Sin 2 where x is in cm and t in sec With respect to this motion identify the correct option 1 Motion is SHM of amplitude 2 cm time period 2 sec and initial phase of 3 2 2 Motion is SHM of amplitude 2 cm time period 2 sec and initial phase of zero 3 Motion is SHM of amplitude 4 cm time period 1 sec and initial phase of zero

A mass of 1 kg is attached to two identical springs each with stiffness k 20 kN m as shown in the figure Under frictionless condition the natural frequency of the system in Hz is close to k ww k Ho 1 kg

a where k and a are positive 2 2x particle of mass m is moving in potential energy U onstants The angular frequency of small oscillations for the simple harmonic motion of the particle about a stable equilibrium position is A k Vm B 2k m C 2 LE m kx D 4 k m

A pendulum clock keeps correct time at 0 C It s mean coefficient of linear expansion is a C then the loss in seconds per day by the clock if the temperature rises by t C is 1 atx864000 at 2 1 1 1 at 2 atx86400 atx86400 atx8 at a 2

to 4 34 A ho zonta supported by two vertical identical springs of spring constant K each and natural length lo A current i is flowing in the rod in the direction shown if the rod is in equilibrium then the length of each spring in this state is m A ellele ilB mg K mg ilB B Figure 4 227 B D K reeeeee ilB mg 2K mg ilB

13 If a particle executes SHM with angular velocity 3 5 rad s and maximum acceleration 7 5m s then the amplitude of oscillation will be a 0 8 m b 0 69 m c 0 41 m d 0 61 m am s and 7 cm

Figure shows a small block of mass m attached to a spring of force constant k and an identical spring hangs from ceiling Initially lower spring is in compressed state with compressed state with compression equal to 3mg from k natural length of spring When block is released it strikes upper spring and sticks to it What is the amplitude of oscillation in cm after sticking given mg 10 N k 100 7 N m wwwwwww Equilibrium position www mg k

If a positively charged pendulum is oscillating in a uniform electric field as shown in fig Its time period as compared to that when it was uncharged 1 Will increase 2 Will decrease 3 Will not change 4 Will first increase then decrease Report your answer in integer 1 2 3 4 by checking above option

Objective Question II One or more correct option 7 A simple pendulum of length L and mass bob M oscillating in a plane about a vertical line between angul limits and o For an angular displacement 8 101 the tension in the string and the velocity of the bob are T and respectively The following relations hold good under t above conditions 1986 2 a T cos 0 Mg b T Mgcos 0 My L c The magnitude of the tangential acceleration of the be ar g sin e d T Mg cos 0

36 Time period of a simple pendulum of length L as measured in an elevator descending with acceleration is 3 a 2 c 2 3L 2g 3L g 6 0 b r d 2n 3L g 2L 30

executing SHM is 0 then the time period of the body is a Zero b 2 The mass and dian d TC 2 2d x dt 32x

40 A mass m is suspended by means of two coiled springs which have the same length in unstretched condition as shown in figure Their force constants are k and k respectively When set into vertical vibrations the period will be 2 c 2 k k m k k A 00000 F b 2 m d 2n B 00000 F k k m

8 Assertion If the amplitude of a simple harmonic is doubled its total energy also becomes oscillator doubled Reason The total energy is directly proportional to the amplitude of vibration of the harmonic oscillator

21 A uniform 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 1 nl 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 2 c T 2T mn K n 1 m nKo b T 2 d T 2n m K n 1 m n 1 Kn

19 A simple pendulum of length 1 and mass bob m is suspended vertically The string makes an angle 0 with the vertical The restoring force acting on the pendulum is a mg tan 0 c mg sin 0 b mg sin 0 d mg cos 0

24 The time period of a simple pendulum inside a stationary lift is 5 What will be the time period when the lift moves upwards with an acceleration 4 a 5s b 2 5s 2 5s d 2 s

ent of Onic of a particle The sense of revolution and radius of the circle the period the initial position are indicated on the figure The simple harmonic motion of the x projection of the radius vector of the rotating particle P is a x t B sin b x t B cos c x 1 B sin 9 The boid x t B cos 2 t 30 Tut 15 t TC 15 2 Tt T 15 2 B P t 0 T 30s X

10 Assertion The graph of total energy of a particle in S H M w r t position is a straight line with zero slope Reason Total energy of particle in S H M remains constant throughout its motion

Three simple harmonic motions in the same direction having the same amplitude A and same period are superposed If each differs in phase from the next by 450 then 1 the resultant amplitude is 1 3 A 3 the energy associated with the resulting motion is 3 2 2 times the energy associated with any single motion 4 the phase of the resultant motion relative to the first is 90 9 2 the resulting motion is not simple harmonic

16 A string has tension T for tripling the frequency the tension in the string will be T a 3T 9 C T own mubom b d 9T

If this body rolls purely then time period of its small oscillations is T It s moment of inertia about CM is 9 40 kg m Fill value of T 75 k 200N m v o r r r o oooooooooo a k 200N m mmmmmmmmm b m 1kg a 1m b 3m

a ed 37 A block of mass m and charge q is placed in electric 3y field E Eo 4 where y is a vertical distance ho from the starting point as figure Then ho 9 m Time period T 2n a If mass is released from rest then it will oscillates with mho V3qEo E E 4 b With time period T 2 c With time period T 3y 4 3 ho mho 3qEo mho 3qEo m 4qEo m 4qEo g

A 1 00 x 10 2 kg particle is vibrating in simple harmonic motion with a time period of 1 00 x 10 5 sec and a maximun speed of 1 00 x 10 3 m s The maximum displacement of th particle is 1 59 nm 1 59 m 1 59 mm None of these

23 A particle is undergoing simple harmonic motion on a straight line of amplitude 1 cm and time period 8 second Starting from mean position the distance covered by the particle in first five seconds is approximately 1 2 1 cm 3 2 5 cm 2 2 3 cm 4 2 7 cm dations

A wedge of mass m is kept on smooth surface and connected with two springs as shown in the figure Initially springs are in their natural length Time period of small oscillations of the wadge will be fr eeeee 4k 60 m k Jeeee KV

A plane wave is represented by x 1 2 sin 314t 12 56y Where x and y are distances measured along in x and direction in meters and t is time in seconds This wave has A wavelength of 0 25 m and travels in ve x direction A wavelength of 0 25 m and travels in ve y direction A wavelength of 0 5 m and travels in ve y direction A wavelength of 0 5 m and travels in ve x direction

2 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 a 45 c 60 b 90 d 30

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 direction 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 Find period of small oscillations of the system in the form X And fill value of X g 10m s sec 10 B 1 20 cm Bob

1 A heavy brass sphere is hung from a weightless inelastic spring and as a simple pendulum its time period of oscillation is T When the sphere is immersed in a non viscous liquid of density 1 10 that of brass it will act as a simple pendulum of period a T 10 b T 9 C 9 10 T d 10 T

6 Two linear simple harmonic motion of equal amplitude a frequencies 20 are impressed on a particle along x y axis respectively resultant path followed by particle is given by x y a What is initial phase difference between them A B IN 3x D

3 The relation between acceleration and displacement of four particles are given below a a 2x C c a 2x b a ax d a 2x 2x Which one of the particle is exempting simple harmonic motion

15 When the kinetic energy of a body executing SHM is 1 3 of the potential energy The displacement of the body is x percent of amplitude where x is a 51 b 87 c 73 d 13 6 How long after the beginning of motion ie 1 S 2 F 3

In the overhead view of above figure a long uniform rod of mass 0 600kg is free to rotate in a horizontal plane about a vertical axis through its center A spring with force constant k 1850N m is connected horizontally between one end of the rod and a fixed wall When the rod is in equilibrium it is parallel to the wall What is the period of the small oscillations that result when the rod is rotated slightly and released Wall oooo

7 The motion of a particle executing simple harmonic motion is described by the displacement function x t A cos wt p If the initial t 0 position of the particle is 1 cm and its initial velocity is cm s what are its amplitude and initial phase angle The angular frequency of the particle is ns If instead of the cosine function we choose the sine function to describe the SHM x B sin at a what are the amplitude and initial phase of the particle with the above initial conditions fuam 0 to 50 kg The length of the scale is 20

21 If the two S H M s are having same period along same path and amplitude is same but different initial phases the resultant amplitude when two S H M s are out of phase n is a double b same c zero d infinity

A homogeneous disk is allowed to swing in a vertical plane about the pivot shown below Compute the following quantities showing steps in detail don t copy ready formulas 1 The moment of inertia about the center of mass by direct integration 2 The moment of inertia about the pivot 3 The radius of gyration about the pivot 4 The period of oscillations 5 The center of oscillations for the pivot Pivot

A uniform rod of length 6m is hanged vertically from one end and given a small angular displacement from mean position then it starts performing angular SHM calculate the time period of that SHM Take g

A block of mass m is tied to one end of a spring which passes over a smooth fixed pulley A and under a light smooth movable pulley B The other end of the string is attached to the lower end of a spring of spring constant K2 find the period in s of small oscillation of mass m about its equilibrium position Take 2 m 7 kg K 4K K 17 N m B O A E

The phase at a time t of a particle in simple harmonic motion tells Only the position of the particle at time t Only the direction of motion of the particle at time t Both the position and direction of motion of the particle at time t Neither the position of the particle nor its direction of motion at time t

A particle is moving with constant angular velocity along the circumference of a circle Which of the following statements is true The particle so moving executes S H M The projection of the particle on any one of the diameters executes S H M The projection of the particle on any of the diameters executes S H M None of these

A particle is executing simple harmonic motion with a period of T seconds and amplitude a metre The a shortest time it takes to reach a point m from its mean position in seconds is T T 4 T 8