CBSE Class 11 Oscillations Worksheet A

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Question. A simple pendulum has a metal bob, which is negatively charged. If it is allowed to oscillate above a positively charged metallic plate, then its time period will
(a) increase
(b) decrease
(c) become zero
(d) remain the same

Answer: B

Question. A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency w. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
(a) at the mean position of the platform
(b) for an amplitude of g/ω2
(c) for an amplitude of g²/ω²
(d) at the highest position of the platform 

Answer: B

Question. A simple spring has length l and force constant K. It is cut into two springs of lengths l₁ and l₂ such that l₁ = nl₂ (n = an integer). The force constant of spring of length l₁ is
(a) K (1 + n)
(b) (K/n) (1 + n)
(c) K
(d) K/(n + 1)

Answer: B

Question. The potential energy of a particle (Ux) executing S.H.M. is given by
(a) U_x = k/2 (x - a)²
(b) U_x = k₁x + k₂ x² + k₃x³
(c) U_x = Ae^-bx
(d) U_x = a constant

Answer: A

Question. Two simple pendulums of length 0.5 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 [nT₁=(n–1)T₂, where T1 is time period of shorter length & T₂ be time period of longer wavelength and n are no. of oscillations completed]
(a) 5
(b) 1
(c) 2
(d) 3

Answer: B

Question. If the magnitude of displacement is numerically equal to that of acceleration, then the time period is
(a) 1 second
(b) π second
(c) 2π second
(d) 4π second

Answer: C

Question. The graph shown in figure represents 
(a) motion of a simple pendulum starting from mean position
(b) motion of a simple pendulum starting from extreme position
(c) simple pendulum describing a horizontal circle
(d) None of these

Answer: A

Question. A particle executing simple harmonic motion along y-axis has its motion described by the equation y = Asin(ωt) + B. The amplitude of the simple harmonic motion is
(a) A
(b) B
(c) A + B
(d) √A+ B

Answer: A

Question. Resonance is an example of
(a) tuning fork
(b) forced vibration
(c) free vibration
(d) damped vibration

Answer: B

Question. A child swinging on swing in sitting position stands up.
The time period of the swing will
(a) increase
(b) decrease
(c) remain same
(d) increase if the child is tall and decrease if the child is short.

Answer: B

Question. The graph of time period (T) of simple pendulum versus its length (l) is 

Answer: A

Question. A particle of mass 10 gm is describing S.H.M. along a straight line with period of 2 sec and amplitude of 10 cm. Its kinetic energy when it is at 5 cm from its equilibrium position is
(a) 37.5π² erg
(b) 3.75π² erg
(c) 375π² erg
(d) 0.375π² erg

Answer: C

Question. 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)
(a) 5
(b) 5 √2
(c) 5 √3
(d) 10 √2

Answer: C

Question. Out of the following functions, representing motion of a particle, which represents SHM?
(A) y = sinωt - cosωt
(B) y = sin³ ωt
(C) y = 5 cos(3π/4 - 3ωt)
(D) y = 1+ ωt + ω²t²
(a) Only (A)
(b) Only (D) does not represent SHM
(c) Only (A) and (C)
(d) Only (A) and (B)

Answer: C

Question. A clock which keeps correct time at 20ºC, is subjected to 40ºC. If coefficient of linear expansion of the pendulum is 12 × 10^–6 per ºC. How much will it gain or loose in time ?
(a) 10.3 seconds/day
(b) 20.6 seconds/day
(c) 5 seconds/day
(d) 20 minutes/day

Answer: A

Question. The tension in the string of a simple pendulum is
(a) constant
(b) maximum in the extreme position
(c) zero in the mean position
(d) None of these

Answer: D

Question. A rectangular block of mass m and area of cross-section A floats in a liquid of density r . If it is given a small vertical displacement from equilibrium. It undergoes oscillations with a time period T then
(a) T∝ m
(b) T∝ r
(c) T∝ 1/A
(d) T∝ 1/ r

Answer: A

Question. In the fig. S₁ and S₂ are identical springs. The oscillation frequency of the mass m is f. If one spring is removed, the frequency will become
(a) f
(b) f × 2
(c) f x √2
(d) f / √2

Answer: D

Question. The displacement of aparticle along the x-axis is given by x = a sin² ωt. 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

Answer: A

Question. 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
(a) T
(b) T / √2
(c) 2T
(c) √2 T

Answer: D
 

1. The girl sitting on a swing stands up. What will be the effect on periodic time of swing?

2. At what distance from the mean position, is the kinetic energy in a simple harmonic oscillator equal to potential energy?

3. A simple harmonic oscillator is represented by the equation : Y = 0.40 Sin(440t+0.61) Y is in metres t is in seconds

Find the values of 1) Amplitude 2) Angular frequency 3) Frequency of oscillation

4) Time period of oscillation, 5) Initial phase.

4. The soldiers marching on a suspended bridge are advised to go out of steps. Why?                       

 5. The springs of spring factor k, 2k, k respectively are connected in parallel to a mass m. If the mass = 0.08kg m and k = 2N|m, then find the new time period?

6. The bob of a vibrating simple pendulum is made of ice. How will the period of swing will change when the ice starts melting?

 7. An 8 kg body performs S.H.M. of amplitude 30 cm. The restoring force is 60N, when the displacement is 30cm. Find: - a) Time period b) the acceleration c) potential and kinetic energy when the displacement is 12cm?

8. What is Simple pendulum? Find an expression for the time period and frequency of a simple pendulum?

9. A particle executing SH.M has a maximum displacement of 4 cm and its acceleration at a distance of 1 cm from its mean position is 3 cm/s². What will be its velocity when it is at a distance of 2cm from its mean position?

10. What is ratio of frequencies of the vertical oscillations when two springs of spring constant K are connected in series and then in parallel?

11. The kinetic energy of a particle executing S.H.M. is 16J when it is in its mean position. If the amplitude of oscillations is 25cm and the mass of the particle is 5.12kg. Calculate the time period of oscillations?

Click on link below to download CBSE Class 11 Oscillations Worksheet A.