## NEET AIPMT Physics Chapter Wise Solutions – Oscillations

Contents

NEET AIPMT Physics Chapter Wise SolutionsBiology Chemistry

**1. A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is**

(a) 10.5 Hz

(b) 105 Hz

(c) 155 Hz

(d) 205 Hz **(AIPMT 2015)**

**2. A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then, its time period of vibration will be**

**3. A particle is executing SHM along a straight line. Its velocities at distances x _{1} and x_{2} from the mean position are V_{1 }and V_{2}, respectively. Its time period i is**

**4. When two displacements represented by y _{1} = a sin(ωt) and y_{2} = b cos(ωt) are superimposed the motion is**

**5. The oscillation of a body on a smooth horizontal surface is represented by the equation,**

**X = A cos(ωt)**

** where X = displacement at time ‘ t ’**

**ω = frequency of oscillation**

** Which one of the following graphs shows correctly the variation a with t ?**

**6. A particle of mass m oscillates along x-axis according to equation x = asincof. The nature of the graph between momentum and displacement of the particle is**

(a) Circle

(b) Hyperbola x

(c) Ellipse

(d) Straight line passing through origin **(Karnataka NEET 2013)**

**7. Out of the following functions representing motion of a particle which represents SHM**

**8. 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 mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is**

**9. The displacement of a particle along the x axis is given by x = asin ^{2}ωy. The motion of the particle corresponds to**

(a) simple harmonic motion of frequency ω/π

(b) simple harmonic motion of frequency 3ω/2π

(c) non simple harmonic motion

(d) simple harmonic motion of frequency ω/2π

**(Prelims 2010)**

**10. 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 will now be**

**11. A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T. The speed of the pendulum at x = a/2 will be**

**12. Which one of the following equations of motion represents simple harmonic motion?**

**13. Two simple harmonic motions of angular frequency 100 and 1000 rad s ^{-1} have the same displacement amplitude. The ratio of their maximum acceleration is**

(a) 1:10

^{3}

(b) 1:10

^{4}

(c) 1:10

(d) 1:10

^{2}

**(Prelims 2008)**

**14. A particle executes simple harmonicXoscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is**

(a) T/8

(b) T/12

(c) T/2

(d) T/4.

**15. A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible.
When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take g = 10 m/s ^{2}).**

(a) 10.0 cm

(b) any value less than 12.0 cm

(c) 4.0 cm

(d) 8.0 cm.

**(2007)**

**16. The particle executing simple harmonic motion has a kinetic energy 7if0cos2(Ot. The maximum values of the potential energy and the total energy are respectively**

(a) K_{0}/2 and K_{0}

(b) K_{0} and 2K_{0}

(c) K_{0} and K_{0}

(d) 0 and 2K_{0}.** (2007)**

**17. The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is**

(a) π

(b) 0.707π

(c) zero

(d) 0.5π.** (2007)**

**18. A rectangular block of mass m and area of cross section A floats in a liquid of density p. If it is given a small vertical displacement from equilibrium it undergoes with a time period T, then**

**19. The circular motion of a particle with constant speed is**

(a) periodic but not simple harmonic

(b) simple harmonic but not periodic

(c) period and simple harmonic

(d) neither periodic not simple harmonic. **(2005)**

**20. A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is**

(a) 4 Hz

(b) 3 Hz

(c) 2 Hz

(d) 1 Hz. **(2004)**

**21. Two springs of spring constants k _{1} and k_{2} are joined in series. The effective spring constant of the combination is given by**

**22. Which one of the following statements is true for the speed v and the acceleration a of a particle executing simple harmonic motion ?**

(a) When v is maximum, a is maximum.

(b) Value of a is zero, whatever may be the value of v.

(c) When v is zero, a is zero.

(d) When v is maximum, a is zero. **(2003)**

**23. The potential energy of a simple harmonic oscillator when the particle is half way to its end point is**

**24. A particle of mass m oscillates with simple harmonic motion between points x _{1} and x_{2}, the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph**

**25. The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be **

(a) T/4

(b) T

(c) T/2

(d) 2T **(2003)**

**26. 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** (2003)**

**27. Displacement between maximum potential energy position and maximum kinetic energy postion for a particle executing simple harmonic motion is**

(a) ± a/2

(b) +a

(c) ±a

(d) -1. **(2002)**

**28. When an oscillator completes 100 oscillations its amplitude reduced to of initial value. What will be its amplitude, when it completes 200 oscillations?**

**29. A mass is suspended separately by two different springs in successive order then time periods is t _{1} and t_{2} respectively. If it is connected by both spring as shown in figure then time period is t0, the correct relation is**

**30. The total energy of particle performing SHM depend on**

(a) k, a, m

(b) k, a

(c) k, a, x

(d) k, x. **(2001)**

**31. Two masses M _{A} and M_{B} are hung from two strings of length l_{A} and l_{B} respectively. They are executing SHM with frequency relation f_{A}= 2f_{B}, then relation**

**32. The bob of simple pendulum having length l, is displaced from mean position to an angular position q with respect to vertical. If it is released, then velocity of bob at equilibrium position**

**33. Time period of a simple pendulum is 2 sec. If its length is increased by 4 times, then its period becomes**

(a) 8 sec

(b) 12 sec

(c) 16 sec

(d) 4 sec **(1999)**

**34. A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force F sinωt. If the amplitude of the particle is maximum for ω =ω _{1} and the energy of the particle maximum for ω = ω2, then**

(a) ω

_{1}≠ ω

_{0}and ω

_{2}= ωo

(b) ω

_{1}= ω

_{0}and ω

_{2}= ω

_{0}

(c) ω

_{1}= ω

_{0}and ω

_{2}≠ ω

_{0}

(d) ω

_{1}≠ ω

_{0 }and ω

_{2}≠ ω

_{0}

**(1989, 1998)**

**35. Two simple pendulums of length 5 m and 20 m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed oscillations.**

(a) 2

(b) 1

(c) 5

(d) 3 **(1998)**

**36. A mass m is vertically suspended from a spring of negligible mass; the system oscillates with a frequency n. What will be the frequency of the system, if a mass 4 m is suspended from the same spring?**

(a)

(b) 4n

(c)

(d) 2n** (1998)**

**37. If the length of a simple pendulum is increased by 2%, then the time period**

(a) increases by 1%

(b) decreases by 1%

(c) increases by 2%

(d) decreases by 2%. **(1997)**

**38. Two SHM’s with same amplitude and time period, when acting together in perpendicular directions with a phase difference of π/2, give rise to**

(a) straight motion

(b) elliptical motion

(c) circular motion

(d) none of these. **(1997)**

**39. A particle starts with S.H.M. from the mean position as shown in the figure. Its amplitude is A and its time period is T. At one time, its speed is half that of the maximum speed. What is this displacement?**

**40. A linear harmonic oscillator of force constant 2 x 10 ^{6} N/m and amplitude 0.01 m has a total mechanical energy of 160 J. Its**

(a) P.E. is 160 J

(b) P.E. is zero

(c) P.E. is 100 J

(d) P.E. is 120 J.

**(1996)**

**41. A simple pendulum with a bob of mass m oscillates from A to C and back to A such that PB is H. If the acceleration due to gravity is g, then the velocity of the bob as it passes through B is**

**42. In a simple harmonic motion, when the displacement is one-half the amplitude, what fraction of the total energy is kinetic?**

(a) 1/2

(b) 3/4

(c) zero

(d) 1/4. **(1995)**

**43. A body of mass 5 kg hangs from a spring and oscillates with a time period of 2% seconds. If the ball is removed, the length of the spring will decrease by**

(a) g/k metres

(b) k/g metres

(c) 2π metres

(d) g metres. **(1994)**

**44. A particle executes S.H.M. along x-axis. The force acting on it is given by**

(a) A cos (kx)

(b) Ae^{-Kx}

(c) Akx

(d) – Akx.** (1994, 88)**

**45. A seconds pendulum is mounted in a rocket. Its period of oscillation will decrease when -rocket is**

(a) moving down with uniform acceleration

(b) moving around the earth in geostationary orbit

(c) moving up with uniform velocity

(d) moving up with uniform acceleration. **(1994)**

**46. A loaded vertical spring executes S.H.M. with a time period of 4 sec. The difference between the kinetic energy and potential energy of this system varies with a period of**

(a) 2 sec

(b) 1 sec

(c) 8 sec

(d) 4 sec.** (1994)**

**47. A body executes simple harmonic motion with an amplitude A. At what displacement from the mean position is the potential energy of the body is one fourth of its total energy ?**

(a) A/4

(b) A/2

(c) 3A/4

(d) Some other fraction of A **(1993)**

**48. A simple harmonic oscillator has an amplitude A and time period T. The time required by it to travel from X= A to A = A/2 is**

(a) T/6

(b) T/4

(c) T/3

(d) T/2 **(1992)**

**49. If a simple harmonic oscillator has got a displacement of 0.02 m and acceleration equal to 0.02 m/s ^{2} at any time, the angular frequency of the oscillator is equal to**

(a) 10 rad/s

(b) 0.1 rad/s

(c) 100 rad/s

(d) 1 rad/s

**(1992)**

**50. A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration a, then the time period is given by where g is equal to given by T=2π,where g is equal to**

**51. A body is executing simple harmonic motion. When the displacements from the mean position is 4 cm and 5 cm, the corresponding velocities of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is**

(a) 2π sec

(b) π/2 sec

(c) π sec

(d) (3π/2) sec** (1991)**

**52. The angular velocity and the amplitude of a simple pendulum is ω and a respectively. At a displacement* from the mean position if its kinetic energy is T and potential energy is V, then the ratio of T to V is**

**53. The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of π results in the displacment of the particle along**

(a) circle

(b) figure of eight

(c) straight line

(d) ellipse **(1990)**

**54. A mass m is suspended from the two coupled springs connected in series. The force constant for springs are k _{1 }and k_{2}. The time period of the suspended mass will be**

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