CBSE Class 11 Oscillations Worksheet C

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Question. A vertical mass-spring system executes simple harmonic oscillations with a period of 2s. A quantity of this system which exhibits simple harmonic variation with a period of 1 s is
(a) velocity
(b) potential energy
(c) phase difference between acceleration and displacement
(d) difference between kinetic energy and potential energy

Answer: B

Question. A particle of mass is executing oscillations about the origin on the x-axis. Its potential energy is V(x) = k | x |³, where k is a positive constant. If the amplitude of oscillation is a, then its time period T is
(a) proportional to 1/√a 
(b) proportional to √a
(c) independent a^3/2
(d) None of these

Answer: A

Question. The graph shown in figure represents
(a) S.H.M.
(b) circular motion
(c) rectillinear motion
(d) uniform circular motion

Answer: A

Question. An instantaneous displacement of a simple harmonic oscillator is x = A cos (ωt + π/4). Its speed will be maximum at time
(a) π/4 ω
(b) π/2 ω
(c) π/ω
(d) 2 π/ω

Answer: A

Question. Frequency of oscillation is proportional to 

Answer: A

Question. A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k'' . Then k' : k'' is 
(a) 1 : 9
(b) 1 : 11
(c) 1 : 14
(d) 1 : 6

Answer: B

Question. The equation of SHM of a particle is A + 4π²x = 0 where a is instantaneous linear acceleration at displacement x. The frequency of motion is
(a) 1 Hz
(b) 4π Hz
(c) 1/4 Hz
(d) 4 Hz

Answer: A

Question. The graph plotted between the velocity and displacement from mean position of a particle executing SHM is
(a) circle
(b) ellipse
(c) parabola
(d) straight line

Answer: B

Question. Acceleration of a particle executing SHM, at it’s mean position is
(a) infinity
(b) variable
(c) maximum
(d) zero

Answer: D

Question. A particle executes S.H.M. having time period T, then the time period with which the potential energy changes is
(a) T
(b) 2 T
(c) T/2
(d) ∞

Answer: C

Question. A simple pendulum attached to the roof of a lift has a time period of 2s in a stationary lift. If the lift is allowed to fall freely the frequency of oscillations of pendulum will be
(a) zero
(b) 2 Hz
(c) 0.5 Hz
(d) infinity

Answer: A

Question. The displacement of a S.H.M. doing particle when K.E. = P.E. (amplitude = 4 cm) is
(a) 2 √2 cm
(b) 2 cm
(c) 1/√2 cm
(d) √2 cm

Answer: A

Question. Two oscillators are started simultaneously in same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest to
(a) 2%
(b) 1%
(c) 0.5%
(d) 0.25%

Answer: B

Question. In the figure shown, the spring is light and has a force constant k. The pulley is light and smooth and the strring is light . The suspended block has a mass m. On giving a slight displacement vartically to the block in the downward direction from its equilibrium position the block executes S.H.M. on being released with time period T. Then 

Answer: D

Question. When an oscillator completes 100 oscillations its amplitude reduces to 1/3 of its initial value. What will be its amplitude, when it completes 200 oscillations ?
(a) 1/8
(b) 2/3
(c) 1/6
(d) 1/9

Answer: D

Question. A rod is hinged vertically at one end and is forced to oscillate in a vertical plane with hinged end at the top, the motion of the rod:
(a) is simple harmonic
(b) is oscillatory but not simple harmonic
(c) is pericolic but not oscillatory
(d) may be simple harmonic

Answer: D

Question. 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 directions, each time their displacement is half of their amplitude. What is the phase difference between them ?
(a) 5 p/6
(b) 2 π/3
(c) π/3
(d) π/6

Answer: B

Question. A particle of mass m is fixed to one end of a light spring of force constant k and unstretched length l. The system is rotated about the other end of the spring with an angular velocity w, in gravity free space. The increase in length of the spring will be 

Answer: B

Question. A straight rod of negligible mass is mounted on a frictionless pivot and masses 2.5 kg and 1 kg are suspended at distances 40 cm and 100 cm respectively from the pivot as shown. The rod is held at an angle q with the horizontal and released. Then
(a) the rod executes periodic motion about horizontal position after the release
(b) the rod remains stationary after the release.
(c) the rod comes to rest in vertical position with 2.5 kg mass at the lowest point
(d) the rod executes periodic motion about vertical position after the release

Answer: B

Question. A particle is executing a simple harmonic motion. Its maximum acceleration is a and maximum velocity is b. Then its time period of vibration will be :
(a) α/β
(b) β²/α
(c) 2πβ/α
(d) β²/α²

Answer: C

Question. 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 S.H.M. is
(a) 1.05 s
(b) 0.52 s
(c) 0.25 s
(d) 0.03 s

Answer: D

Question. A pendulum bob is raised to a height h and released from rest. At what height will it attain half of its maximum speed?
(a) 3h/4
(b) h/2
(c) h/4
(d) 0.707h

Answer: A

Question. A mass m fall on spring of spring constant k and negligible mass from a height h. Assuming it sticks to the pan and executes simple harmonic motion, the maximum height upto which the pan will rise is

Answer: B

Question. A boy is executing simple Harmonic Motion. At a displacement x its potential energy is E₁ and at a displacement y its potential energy is E₂. The potential
energy E at displacement (x + y) is
(a) √E = √E₁ - √E₂
(b) √E = √E₁ + √E₂
(c) E = E₁ + E₂
(d) E = √E₁ - E₂

Answer: B

Question. A mass is suspended separately by two different springs in successive order then time periods is t₁ and t₂ respectively. It is connected by both springs as shown in fig. then time period is t₀, the correct relation is
(a) t₀² = t₁2 + t₂²
(b) t₀-2 = t₁-2 + t₂-2
(c) t₀^-1 = t₁^-1 + t₂^-1
(d) t₀ = t₁ + t₂

Answer: B
 

1. What is the relation between uniform circular motion and S.H.N?

2. What is the minimum condition for a system to execute S.H.N?

3. A particle executing S.H.N. along a straight line has a velocity of um/s when its displacement from mean position is 3 m and 3 m / s when displacement is 4m. Find the time taken to travel 2.5 m from the positive extremity of its oscillation?

4. Springs is spring constant K, 2K, 4K, K ----- are connected in series. A mass M Kg is attached to the lower end of the last spring and system is allowed to vibrate. What is the time period of oscillation?

5. A particle is moving with SHN in a straight line. When the distance of the particle from mean position has values x1 and x2 the corresponding values of velocities are v1 and v2. Show that the time period of oscillation is given by:

6. A mass = m suspend separately from two springs of spring constant k1 and k2 gives time period t1 and t2 respectively. If the same mass is connected to both the springs as shown in figure. Calculate the time period ‘t’ of the combined system?

7. Show that the total energy of a body executing SHN is independent of time? 

8. A particles moves such that its acceleration ‘a’ is given by a = -b x where x = displacement from equilibrium position and b is a constant. Find the period of oscillation?

9. A particle is S.H.N. is described by the displacement function: →

If the initial (t = 0) position of the particle is 1 cm and its initial velocity is π cm | s, What are its amplitude and phase angle?

10. Determine the time period of a simple pendulum of length = l when mass of bob = m Kg?

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