1. OBJECTIVE QUESTIONS
FOR
NEET AIIMS JIPMER

2. PHYSICS OSCILLATION SET 1 MCQ’S

3. Q1. Two particles are executing S. H. M
Q1. Two particles are executing S.H.M. of same amplitude and Frequency along the same straight line path. They pass each other when going in opposite direction, each time their displacement is half of their amplitude. What is the phase difference between them?

4. ANSWER (B) EXPLANATION

5. Q2. The displacement of two particles executing SHM are represented by equations 𝑦 1 =2 𝑠𝑖𝑛 10𝑡+𝜃 , 𝑦 2 =3 𝑐𝑜𝑠 10 𝑡. The phase difference between the velocity of these particles is: θ −θ
θ+π/2
θ−π/2

6. ANSWER (D) EXPLANATION

7. Q3. Two pendulums have time period T and 5 T/4. They start S. H. M
Q3. Two pendulums have time period T and 5 T/4. They start S.H.M. at the same time from the mean position. What will be the phase difference between them after the bigger pendulum completed one oscillation ?
45o
90o
60o
30o

8. ANSWER (B) EXPLANATION
When bigger pendulum of time period (5 T/4) completes one vibration, the smaller pendulum will complete (5/4) vibrations.
It means the smaller pendulum, will be leading the bigger pendulum by phase T/4 sec = 𝜋 2 𝑟𝑎𝑑=90o.

9. Q4. A particle executes S. H. M
Q4. A particle executes S.H.M. then the graph of velocity as a function of displacement is :
A straight line
A circle
An ellipse
A hyperbola

10. ANSWER (C) EXPLANATION

11. Q5. Acceleration (a) –displacement (x) graph of a particle executing SHM is as shown in figure. The time period of its oscillation is sec is :
π 4
π 2 π 2π

12. ANSWER (D) EXPLANATION

13. Q6. A body of mass 5 gram is executing S. H. M. about a fixed point O
Q6. A body of mass 5 gram is executing S.H.M. about a fixed point O. With an amplitude of 10 cm, its maximum velocity is 100 cm/s. Its velocity will be 50 cm 𝒔 −𝟏 𝒂𝒕 𝒂 distance (in cm) 5
5 2
5 3
10 2

14. ANSWER (C) EXPLANATION

15. Q7. A coin is placed on a horizontal platform, which undergoes horizontal SHM about a mean position O. The coin placed on platform does not slip, when angular frequency of the SHM is 𝝎. The coefficient of friction between the coin and the platform is 𝝁. The amplitude of oscillation is gradually increased. The coil will begin to slip on the platform for the first time,
At the mean position
At the extreme position of oscillation
For an amplitude of 𝜇 𝑔/ 𝜔 2
For an amplitude of 𝑔/𝜇 𝜔 2

16. ANSWER (C) EXPLANATION
Let O be the mean position and 𝑥 be the distance of coin from O. The coin will slip if centrifugal force on coin just becomes equal to force of friction, i.e., 𝑚𝑥 𝜔 2 =𝜇 𝑚𝑔
The coin will slip if 𝑥= maximum = amplitude A.

17. Q8. A horizontal plank has a rectangular block placed on it
Q8. A horizontal plank has a rectangular block placed on it. The plank start oscillating vertically and simple harmonically with an amplitude of 40 cm. the block just loses contact with the plank when the later is momentary at rest. Then
The period of oscillation is 2𝜋/5 𝑠𝑒𝑐
The block weighs double its weight when the plank is at one of the positions of momentary at rest
The block weighs 1.5 times its weight on the plank half way down
The block weighs its true weight on the plank when the latter moves fastest

18. ANSWER (B) EXPLANATION
At one of the extreme position, wt of block = restoring force.
At the other extreme position wt of block and restoring force both act downward directions.
So the wt of block there is double than its weight.

19. Q9. Maximum speed of a particle in SHM is 𝒗 𝒎𝒂𝒙
Q9. Maximum speed of a particle in SHM is 𝒗 𝒎𝒂𝒙. Then average speed of a particle is SHM is equal to :

20. ANSWER (D) EXPLANATION
Let r be the amplitude of oscillation and T be the time period in SHM. Then total distance travelled in time T = 4 r.

21. Q10. The bob of a simple pendulum of length L is released at time t = 0 from a position of small angular displacement. Its linear displacement at time t is given by :

22. ANSWER (D) EXPLANATION
As the bob of simple pendulum released from the position of small angular displacement, hence when t = 0, the bob is at the extreme position.

23. Q11. The motion of a particle varies with time according to the relation 𝒚=𝒂 𝒔𝒊𝒏 𝝎𝒕+𝒃 𝒄𝒐𝒔 𝝎𝒕
The motion of oscillatory but not S.H.M.
The motion is S.H.M. with amplitude a + b
The motion is S.H.M. with amplitude a2+b2
The motion is S.H.M. with amplitude 𝑎 2 + 𝑏 2

24. ANSWER (D) EXPLANATION

25. Q12. 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 displacement of the particle along
Circle
Figure of eight
Straight line
Ellipse.

26. ANSWER (C) EXPLANATION

27. Q13. A mass m = 100 gms is attached at the end of light spring which oscillates on a frictionless horizontal table with an amplitude equal to 0.16 metres and time period equal to 2 sec. Initially the mass is released from rest at t = 0 and displacement 𝒙=−𝟎.𝟏𝟔 𝒎. The expression for the displacement of the mass at any time (t) is :
x=0.16 cos (πt+x)
x=−0.16 cos (πt+x)
x=0.16 cos (πt)
x=−0.16 cos (πt)

28. ANSWER (D) EXPLANATION

29. Q14. If a simple pendulum of length 𝒍 has maximum angular displacement 𝜽, then the maximum kinetic energy of bob of mass m is :

30. ANSWER (C) EXPLANATION

31. Q15. For a simple Harmonic Oscillator, the potential energy is equal to kinetic energy
Once during each cycle
Twice during each cycle
when x=a/2
when x=a

32. ANSWER (B) EXPLANATION
Total energy = P.E. + K.E. When a particle executes S.H.M., there will be two positions in each cycle where the P.E. is equal to K.E. of the body in S.H.M.

33. Q16. For a simple pendulum executing S.H.M. in air, the ratio of K.E. when it passes through the equilibrium position and its P.E. When it has maximum amplitude is :
Less than one
Greater than one
Equal to one
Equal to half

34. ANSWER (B) EXPLANATION
K.E. at the mean position = work done against air friction and gravity. Therefore, K.E. = workdone against air resistance + P.E.
So K.E./P.E. >1.

35. For what value of 𝜔 energy of both the particles is same ?
Q17. The displacement of two identical particles executing SHM are represented by equations 𝑥 1 =8 𝑠𝑖𝑛 10 𝑡+ 𝜋 6 𝑎𝑛𝑑 𝑥 2 =5 𝑐𝑜𝑠 𝜔𝑡 𝑠𝑖𝑛 10 𝑡+ 𝜋 6 𝑎𝑛𝑑 𝑥 2 =5 𝑐𝑜𝑠 𝜔𝑡
For what value of 𝜔 energy of both the particles is same ?
4 units
8 units
16 units
20 units

36. ANSWER (C) EXPLANATION

37. Q18. When the displacement is half of the amplitude, then what fraction of the total energy of a simple harmonic oscillator is kinetic ?
2/7 th
3/4 th
2/9 th
5/7 th

38. ANSWER (B) EXPLANATION

39. Q19. A mass M is suspended from a spring of negligible mass
Q19. A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillation with a time period T. If the mass is increased by m, then the time period becomes 𝟓 𝟒 𝐓 . 𝐓𝐡𝐞 𝐫𝐚𝐭𝐢𝐨 𝐨𝐟 𝐦 𝐌 𝐢𝐬
9/16
5/4
25/16
4/5

40. ANSWER (A) EXPLANATION

41. Q20. For a body of mass m attached to the spring, the spring factor is given by (𝝎, the angular frequency)

42. ANSWER (B) EXPLANATION