Simple harmonic motion Questions and Answers

Two identical simple pendulums A and B are fixed at same point They are displaced by very small angles a and B B a and released from rest Calculate the time period of each ball A E 67 9 B Correct Answer

A loade vertical spring executes S H M with time period of 4 s The difference between the kinetic energy and potential energy of this system varies with a period of 2 s 3 8 s 2 1 s 4 4 s

A loaded vertical spring executes S H M with time period of 4 s The difference between the kinetic energy and potential energy of this system varies with a period of 2 s 3 8 s 2 1s 4 4 s

For a particle undergoing simple harmonic motion the square of velocity v is plotted against square of displacement x 2 The graph obtained will be A parabola An ellipse A straight line A circle

The vertical motion of a ship at sea is described by equation d y dt 4y where y is vertical height of ship in metre above its mean position If it oscillates through height of 1 m Its maximum vertical velocity is 2 ms Its maximum vertical velocity is 1 ms Its maximum vertical acceleration is 16 ms Its minimum vertical acceleration is 10 ms

A mass M is suspended from a spring and oscillates with a period of 0 880 s Each complete oscillation results in an amplitude reduction of a factor of 0 965 due to a small velocity dependent frictional effect Calculate the time it takes for the total energy of the oscillator to decrease to 75 of its initial value

In simple harmonic motion at extreme positions hr min Kinetic energy is maximum and potential energy is minimum Kinetic energy is minimum and potential energy is maximum Both kinetic energy and potential energy are maximum Both potential energy and total mechanical energy are minimum

A particle is executing SHM with amplitude 5 cm about x axis having its mean position at x 0 Speed of particle at x 2 cm and x 3 cm are v and 1 V respectively Value of is V 21 4 T

Acceleration due to gravity of a planet is one fourth that of earth What is period of oscillation of a simple pendulum on this planet if it is 2 s on earth 1s 2 s

Two small blocks of 3 kg and 1 kg are attached to opposite ends of an ideal spring whose spring constant is K 300 Nm as shown in the figure The natural vibration frequency of the system is approximately K 3 kg mmm 1 kg 5 Hz 4 Hz 3 Hz 2 Hz

Two particles executing SHM of same amplitude of 20 cm with same period along the same line about same equilibrium position The maximum distance between the two is 20 cm Their phase difference in radian is equal to

The time period of a spring block system is T The sprin is cut into two parts with their lengths in ratio 2 3 Now the block is attached to smaller part and put to oscillations The ratio of new period to old will be 25 Star 1 52

Consider the following spring mass system The masses m and m2 both are equal to 2 kg If mass m2 is suddenly removed when the system was in equilibrium and in rest then the amplitude of oscillation of the system will be spring constant k 100 N m ellele m m 0 4 m www

Q sur 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 SHM of the block will be ooooooo a of the same frequency and with shifted mean position b of the same frequency and with the same mean position c of changed frequency and with shifted mean position d of changed frequency and with the same mean position

The period of small vertical oscillations of a spring pendulum is found to be equal to 2 s The whole apparatus is now placed in an elevator accelerating upwards with an acceleration 0 5 g The percentage change in the period of the oscillations will be 4 2 3

29 A car is moving along a straight road with a uniform acceleration It passes two points P and Q separated by a distance with velocity 30 km h and 40 km h respectively The velocity of car midway between P and Qis 33 3 km hr b 20 3 km hr 25 2 km hr C a

The equation of a plane progressive harmonic wave is given by y 5 cm sin 2 t 1 5x The maximum medium particle velocity is 10 cm s 15 cm s 10 cm s 20 cm s

35 Figure shows the position time graph of an object in SHM The correct equation representing this motion is x cm 1 2 sin 3 4 sin 2 0 4 2 5 T 6 t t TU 6 TC 3 5 11 2 4 sin t s 4 4 sin 5 6 TU T t 6 6

42 A body of mass 0 01 kg executes simple harmonic motion about x 0 under the influence of a force as shown in figure The time period of SHM is F N 1 1 1 05 s 3 0 25 0 2 80 80 0 2 x m 2 0 52 s nomizor 4 0 03 s

A block of mass M is attached to the lower end of a vertical spring The spring is hung from a ceiling and has force constant value k The mass is released from rest with the spring initially unstretched the maximum extension produced in the length of the spring will be 1 Mg 2k 3 2 Mg k 2 Mg k 4 4 Mg k

In case of a forced vibration the resonance peak becomes very sharp when the a damping force is small b restoring force is small c applied periodic force is small d quality factor is small 7 04 AM

d 0 61 m 23 Two particles are executing simple harmonic motion of the same amplitude A and frequency a along the x axis Their mean position is separated by distance xo xo A If the maximum separation between themis xo A the phase difference between their motions is a c H 37 6 W NEE 20 d KIKIN

The vertical displacement sin wt cos wt 2 y 2 does not lose contact with the platform is g 10 m s y is in m t is in s and w is in rad s rad s 10rad s y of a platform with a body of certain mass placed on it is where w is a constant The maximum value of w such that the body

A block A of mass 1 kg is in contact with another block of same mass A is attached to a spring of natural length I m and spring constant 100 N m The coefficient of friction for both of them is same u 0 2 The spring is initially compressed by 10 cm and released If possible length of the spring is 9x10 cm when both blocks are in contact then the value of n will ha

The time period of a simple pendulum is measured to be equal to 4 s If the string of the pendulum is cut into three parts of lengths in the ratio 1 2 4 and equal masses are hung at their respective ends then the time period of the shortest pendulum will be 4 S 2 s

A ring shaped tube contains equal mass of Oxygen and Nitrogen in section 1 and section 2 respectively separated by a smooth movable conducting piston P2 If P is fixed partition then value of 0 in equilibrium will be 11 P fixed 192 120 168 135 P movable

iii Length of resonance tube is 140 cm How many resonance are possible for wave have wave length 40 cm iv Length of resonance tube is 150 cm How many resonance are possible for wave having frequency

Two particles with same mass are performing simple harmonic motions along x axis whose displacement versus time graphs are shown The ratio of their K maximum kinetic energies K x m 1 1 1 2 1 4 A 2A 1 2 2A is t s

A particle is subjected to two simple harmonic motions along x direction and y direction simultaneously according to equations x 3 sin 2t and y 4 cos 2 t then Motion of particle will be on an ellipse Motion of particle will be on a straight line Motion of particle will be on a circle Motion of particle will be on a hyperbola

Two particles each performing their respective S with same amplitude along the same line start the motion from their common mean position in opposite direction If the frequency of oscillation of one particl is 2 Hz and that of the other particle is 4 Hz then the time after which the particle cross each other is 1 s 6 3 S 4 s S

A particle of mass m oscillates along x axis according to equation x asinot The nature of the graph between momentum and displacement of the particle is a Circle b Hyperbola c Ellipse d Straight line passing through origin

A particle which is executing a linear SHM has an amplitude equal to 4 cm It is observed that when the displacement of the particle from mean position is 2 cm then the speed of the particle is equal to 4 cm s The angular frequency of oscillations of the system is 2 rad s 3 rad s 4 rad s 2 S rad s

In simple harmonic motion which one is incorrect statement Displacement and velocity may be in same direction Velocity and acceleration may be in same direction Displacement and acceleration can never be in same direction Displacement and velocity can never be in same direction

uestion Laurquestionnasroon opcions A 0 C and 0 Onity ONE or these four options is correct Marking scheme 5 If the correct option is selected The figure represents the instantaneous picture of a longitudinal harmonic wave travelling along the negative x axis Identify th correct statement s related to the movement of the points shown in the figure 2 In case if selected typed option is incorrect 0 In case if no response is typed selected b C V

The potential energy U of a particle is given by equation U 2 5x 20 joule The mass of the particle is 0 2 kg then The mean position of particle executing SHM is x 2 m The time period of oscillation is 2 5 second Angular frequency of oscillation is 5 rads 1 Time period of oscillations is 5 second

Consider a harmonic motion in which the force F and the displacement y are related by equation FH M y 1 2 ky It can be approximated FSHM y for small values of y Find out the value of k if FSHM FHM 0 9 for y 0 1 m

A mass m is tethered by a spring of spring constant k to the mid point between two walls separated by a distance d The relaxed length of the spring is zero and collisions of the mass with the walls are completely elastic If the mass is released from its equilibrium position with speed v the time period of its motion is independent of v a for all values of v d c only for v 2 k m dk 2 m b only for v d d only for r a 2 m IISC 2012

45 Consider the situation shown in figure 8 E8 Initially the spring is unstretched when the system is released from rest Assuming no friction in the pulley find the maximum elongation of the spring 100000 E

2 A block of mass 250 g is kept on a vertical spring of spring constant 100 N m fixed from below The spring is now compressed to have a length 10 cm shorter than its natural length and the system is released from this position How high does high does the block rise Take g 10 m s

Two particles A and B are performing SHM along same straight line with same amplitude a and same angular frequency w At t 0 A is at the left extreme and B is at a distance a 2 from mean position to the right of mean position and moving toward mean position Then Their phase difference is Their phase difference is 5TT 3 2 3 Time after which they cross each other is Time after which they cross each other is 2 3w 3w

A particle is oscillating in a straight line about a centre of force O towards which when at a distance x the force is mn x where m is the mass n is a constant The amplitude is a 15 cm When at a distance a 3 2 from O the particle receives a blow in the direction of motion which generates extra velocity na If the velocity is away from O find the new amplitude in cm

In the figure shown a block executes SHM under the influence of two springs on a smooth surface as shown It is found that the time period of oscillation in case a is double that in case b If k is 10 N m what is the value of k in N m k k 60000002 6000 rde m a k 6000000d m 600 b

16 A particle is performing SHM with energy of vibration 90 J and amplitude 6 cm When the particle reaches at distance 4 cm from mean position it is stopped for a moment and then released The new energy of vibration will be

A variable force given by F 8x 16 N is applied on block of mass 2 kg At t 0 particle is at rest at x 5 m Equation of motion of block is given by x 3 cos 2 t x 2 3 cos2t x 23cos2t None of these

A particle performs simple harmonic motion with a time period of 0 2 s If the amplitude of the oscillations is 10 cm and the particle starts from mean positions then the average velocity of the particle in first 0 1 s will be 10 cm s 50 cm s 5 cm s Zero

period 5 8 od of a simple oscillator 1 12 s and its amplitude is 14 m If initially the oscillator is at mean position than the average spee during oscillation will be T f 3 no 255 space

Both the springs shown in figure 5 E2 are unstretched If the block is displaced by a distance x and released what will be the initial acceleration ooooooo m k ooooooo

A travelling disturbance on a string is represented by the equation y 0 2 sin kx At where t is time in second If the wave speed is twice the maximum particle speed then the value of k will be 2 1 2 5

A particle of mass M is performing SHM with amplitude A When the particle was at A 2 and moving away from mean position a block of same mass was kept on it such that is sticks to it A The new amplitude C The new amplitude in 100 V8 7 m mom B The time period remains unchanged D The time period increases

The maximum velocity of a body undergoing simple harmonic motion is 0 04 ms and its acceleration at 0 02 m from the mean position is 0 06ms Its amplitude and time period respectively are 3 21 10 m 3 23s 1 92 10 m 2 82s 3 14x10 m 3 82s 231 10 m 3 63s