Simple harmonics motion/Questions and Answers on harmonics motion

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 1.A student says that he had applied a force F=- k√x on a particle and the particle moved in simple harmonic motion. He refuses to tell whether k is a constant or not. Assume that he has worked only with positive x and no other force acted on the particle. (a) As x increases k increases. (b) As x increases k decreases. (c) As x increases k remains constant. (d) The motion cannot be simple harmonic.

 2. The time period of a particle in simple harmonic motion is equal to the time between consecutive appearances of the particle at a particular point in its motion. This point is (b) an extreme position (a) the mean position (c) between the mean position and the positive extreme (d) between the mean position and the negative. extreme. 

3. The time period of a particle in simple harmonic motion is equal to the smallest time between the particle acquiring a particular velocity v. The value of u is 
(a) Vmax
 (b)0
 (c) between 0 and Vmas   (d) between 0 and -Vmax 

4. The displacement of a particle in simple harmonic motion in one time period is
 (a) A
 (b) 2A
 (c) 4A 
(d) zero.

 5. The distance moved by a particle in simple harmonic motion in one time period is 
(a) A (b) 24 (c) 4A (d) zero. 

6. The average acceleration in one time period in a simple harmonic motion is
(a)Aω²
(b) Aω²/2
(c)Aω²/√2 
 (d) zero. 
7. The motion of particle is given by 
x= Asinωt + cosωt
the motion of the particle is
(a) not simple harmonics
(b) simplecharmonics wuth amplitude A +B
(c)simple harmonics with amplitude A+B/2
(d) simple harmonics with amplitude √A² + B ² 

8. The displacement of a particle is given by r=A(i cosωt+j sinωt). The motion of the particle is (a) simple harmonic (b) on a straight line (c) on a circle (d) with constant acceleration.

9. A particle moves on the X-axis according to the equation. x= A + B sinot. The motion is simple harmonic with amplitude (a) A (b) B (c) A + B (d) √A²+B².

11. The total mechanical energy of a spring-mass system in simple harmonic motion is E=1/2 M ω²A² mo A. Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will (a) become 2E (c) become √2E (b) become E/2 (d) remain E.
 
12.The average energy in one time period in simple harmonic motion is (a) 1 (c) 1/2m ² ωA²
  (b)1/4 mω²A²  
(c)m A²ω²
(d) zero

13. A particle executes simple harmonic motion with a frequency v. The frequency with which the kinetic energy oscillates is (a) v/2 (b) v (c) 2 v (d) zero. 14. A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will (a) remain T (c) become T/2 (b) become 2T (d) become T/N2.

1 5.bodies A and B of equal mass are suspended from two separate massless springs of spring constant k, and k respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of A to that of 
 (a) k₁/k₂ 
(b)  √k₂/k₁
(c) k₂ /k₁
(d) √k₂/k₁
 
16. A spring-mass system oscillates with a frequency v. If it is taken in an elevator slowly accelerating upward, the frequency will
 (a) increase 
(b) decrease
 (c) remain same
 (d) become zero. 
17. A spring-mass system oscillates in a car. If the car accelerates on a horizontal road, the frequency of oscillation will 
(a) increase 
(b)  decrease 
(c)remain same 
(d) become zero. 
18. A pendulum clock that keeps correct time on the earth is taken to the moon. It will run 
(a) at correct rat
(b) 6 times faster
 (c) √6 times faster 
 (d) √6 times slower. 
19. A wall clock uses a vertical spring-mass system to measure the time. Each time the mass reaches an extreme position, the clock advances by a second. The clock gives correct time at the equator. If the clock is taken to the poles it will (a) run slow 
(b) run fast
 (c) stop working  
(d) give correct time. 
20. A pendulum clock keeping correct time is taken to high altitudes, 
(a) it will keep correct time
 (b) its length should be increased to keep correct time
 (c) its length should be decreased to keep correct time
 (d) it cannot keep correct time even if the length is changed.
 21. The free end of a simple pendulum is attached to the ceiling of a box. The box is taken to a height and the pendulum is oscillated. When the bob is at its lowest point, the box is released to fall freely. As seen from the box during this period, the bob will
 (a) continue its oscillation as before
 (b) stop 
(c) will go in a circular path 
(d) move on a straight line.
22. Select the correct statements. 
(a) A simple harmonic motion is necessarily periodic. 
(b) A simple harmonic motion is necessarily oscillatory. 
(c) An oscillatory motion is necessarily periodic. (d) A periodic motion is necessarily oscillatory. 
23 A particle moves in a circular path with a uniform speed. Its motion is
(a) periodic 
(b) oscilatory
 (c) simple harmonic 
(d) angular simple harmonic..  oscillatory
 24. A particle is fastened at the end of a string and is whirled in a vertical circle with the other end of the string being fixed. The motion of the particle is
 (a) periodic
   (b)  oscillatory
 (c) simple harmonic 
  (d) angular simple harmonic. 
25. A particle moves in a circular path with a continuously increasing speed. Its motion is

(a) periodic
(b) oscillatory
 (c) simple harmonic
  (d) none of them.

 26. The motion of a torsional pendulum is
 (a) periodic
 (b) oscillatory
 (c) simple harmonic. 
(d) angular simple harmonic. 
27. Which of the following quantities are always negative in a simple harmonic motion ?
 (a) F⃗.a⃗.
 (b) v⃗.r⃗. 
(c) a⃗.r⃗. 
(d) F⃗.r⃗
NOTE THIS r⃗ means vector dirction.
2 8. Which of the following quantities are always positive in a simple harmonic motion?
 (a) F⃗.a⃗
(b) v⃗.r⃗
(c) a⃗.r⃗
(d) f⃗.r⃗
 29. Which of the following quantities are always zero in a simple harmonic motion? 
 (a) F⃗xa⃗. 
(b) v⃗xr⃗
 (c) a⃗xr⃗
 (d) F⃗xr⃗

30. Suppose a tunnel is dug along a diameter of the earth. A particle is dropped from a point, a distance h directly
above the tunnel. The motion of the particle as seen from the earth is 
(a) simple harmonic
b) parabolic 
 (c) on a straight line 
(d) periodic. 

31) For a particle executing simple harmonic acceleration is proportional to
 (a) displacement from the mean position
 (b) distance from the mean position 
(c) distance travelled since t = 0 
(d) speed. 

32. A particle moves in the X-Y plane according to the equation x=(i⃗+2⃗j) A cosωt. The motion of the particle is
 (a) on a straight line
 (b) on an ellipse
(c) periodic
 (d) simple harmonic.  
33. A particle moves on the X-axis according to the equation x=x₀sin²ωt . The motion is simple harmonic
 (a) with amplitude xo 
(b) with amplitude 2x,
 (c) with time period2π/ω
 (d) with time period π/ω 

34. In a simple harmonic motion 
(a) the potential energy is always equal to the kinetic energy 
(b) the potential energy is never equal to the kinetic energy 

(c) the average potential energy in any time interval is equal to the average kinetic energy in that time interval 
(d) the average potential energy in one time period is equal to the average kinetic energy in this period.
 35. In a simple harmonic motion 
(a) the maximum potential energy equals the maximum kinetic energy
 (b) the minimum potential energy equals the minimum kinetic energy 
(c) the minimum potential energy equals the maximum kinetic energy 
(d) the maximum potential energy equals the minimum kinetic energy. 
36. An object is released from rest. The time it takes to fall through a distance h and the speed of the object as it falls through this distance are measured with a pendulum clock. The entire apparatus is taken on the moon and the experiment is repeated (a) the measured times are same 
(b) the measured speeds are same
 (c) the actual times in the fall are equal 
(d) the actual speeds are equal.

 37. Which of the following will change the time period as they are taken to moon? 
(a) A simple pendulum (b) A physical pendulum. (c) A torsional pendulum (d) A spring-mass system



ANSWERS TO THE OBJECTIVE QUESTIONS
1. (a)          2     (b)       3. (a)   4.  (d)   5(c) 
6.   (d)         7. (d)         8.(c)   9.(b)   10(c)
11. (d)       12.  (a)      13. (c)  14. (d)  15(d)
16.(c)         17.(c)       18. (d)  19. (d)  20(c)
21. (c)       22.(a)       23.(a)   24. (c)    25 (d)
26. (a)     27.(c)       28. (b)      29. (a)   30(c)
31. (a)       32. (a)   33.   (d)    34(d). 35(a)
36(a)       37(a)

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