CBSE Class 11 Oscillations Worksheet B

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Question. A simple pendulum performs S.H.M. about x = 0 with an amplitude a, and time period T. The speed of the pendulum at x = a/2 will be 

Answer: A

Question. Two wires are kept tight between the same pair of supports. The tensions in the wires are in the ratio 2 : 1, the radii are in the ratio 3 : 1 and the densities are in the ratio 1 : 2. The ratio of their fundamental frequencies is
(a) 2 : 3
(b) 2 : 4
(c) 2 : 5
(d) 2 : 6

Answer: A

Question. A particle moves such that its acceleration ‘a’ is given by a = – bx where x is the displacement from equilibrium position and b is constant. The period of oscillation is
(a) 2 π/b
(b) 2π/ √b
(c) √2 π / b
(d) 2√π / b

Answer: B

Question. 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 SHM of time period T. If the mass is increased by m, the time period becomes 5T/3. Then the ratio of m/M is 
(a) 25/9
(b) 16/9
(c) 5/3
(d) 3/5

Answer: B

Question. The time period of the oscillating system (see figure) is

Answer: B

Question. The total mechanical energy of a spring-mass system in simple harmonic motion is E = 1/2 mω² A² . 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
(b) become E/2
(c) become √2E
(d) remain E

Answer: D

Question. A tunnel has been dug through the centre of the earth and a ball is released in it. It executes S.H.M. with time period
(a) 42 minutes
(b) 1 day
(c) 1 hour
(d) 84.6 minutes

Answer: D

Question. A particle of mass 1 kg is moving in S.H.M. with an amplitude 0.02 and a frequency of 60 Hz. The maximum force acting on the particle is
(a) 144 π²
(b) 188 π²
(c) 288 π²
(d) None of these

Answer: C

Question. A body of mass m falls from a height h onto a pan (of negligible mass) of a spring balance as shown. The spring also possesses negligible mass and has spring constant k.
Just after striking the pan, the body starts socillatory motion in vertical directioin of amplitude A and energy E. Then

Answer: B

Question. A pendulum is undergoing S.H.M. The velocity of the bob in the mean position is v. If now its amplitude is doubled, keeping the length same, its velocity in the mean position will be
(a) v/2
(b) v
(c) 2 v
(d) 4 v

Answer: C

Question. y = 2 (cm) sin[πt/2 + Φ] what is the maximum acceleration of the particle doing the S.H.M.
(a) π/2 cm/s²
(b) π²/2 cm/s²
(c) π²/4 cm/s²
(d) π/4 cm/s²

Answer: B

Question. A simple pendulum has time period 't'. Its time period in a lift which is moving upwards with acceleration 3 ms^–2 is 

Answer: A

Question. Which of the following is a simple harmonic motion?
(a) Particle moving through a string fixed at both ends.
(b) Wave moving through a string fixed at both ends.
(c) Earth spinning about its axis.
(d) Ball bouncing between two rigid vertical walls.

Answer: B

Question. 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
(a) 0
(b) 2π/3
(c) π
(d) π/6

Answer: B

Question. If a simple pendulum of length l has maximum angular displacement θ, then the maximum K.E. of bob of mass m is
(a) 1/2 ml / g
(b) mg/ 2l
(c) mgl(1- cos θ)
(d) mgl sin θ/2

Answer: C

Question. Three masses of 500 g, 300 g and 100 g are suspended at the end of a spring as shown, and are in equilibrium. When the 500 g mass is removed, the system oscillates with a period of 2 second. When the 300 g mass is also removed, it will oscillate with a period of 

(a) 2 s
(b) 4 s
(c) 8 s
(d) 1 s 

Answer: D

Question. If the mass shown in figure is slightly displaced and then let go, then the system shall oscillate with a time period of
(a) 2π√m/3k
(b) 2π√3m/2k
(c) 2π√2m/3k
(d) 2π√3k/m 

Answer: B

Question. The length of a second’s pendulum at the surface of earth is 1 m. The length of second’s pendulum at the surface of moon where g is 1/6th that at earth’s surface is
(a) 1/6 m
(b) 6 m
(c) 1/36 m
(d) 36 m

Answer: A

Question. A point particle of mass 0.1 kg is executing S.H.M. of amplitude of 0.1 m. When the particle passes through the mean position, its kinetic energy is 8 × 10^–3 Joule. Obtain the equation of motion of this particle if this initial phase of oscillation is 45º.
(a) y 0.1sin (±4t + π/4)
(b) y 0.2sin (±4t + π/4)
(c) y 0.1sin (±2t + π/4)
(d) y 0.2sin (±2t + π/4)

Answer: A

Question. Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is
(a) x(t) = Bsin (2πt/30)
(b) x(t) = Bcos (πt/30)
(c) x(t) = Bsin (πt/15 +π/2)
(d) x(t) = Bcos (πt/15 +π/2)

Answer: A
 

1. Is the motion of a simple pendulum strictly simple harmonic?

2. Can a simple pendulum experiment be done inside a satellite?

3. Give some practical examples of S. H. M?

4. The time period of a body suspended by a spring is T. What will be the new time period if the spring is cut into two equal parts and 1) the body is suspended by one part. 2) Suspended by both parts in parallel?

5. A simple pendulum is executing Simple harmonic motion with a time T. If the length of the pendulum is increased by 21 %. Find the increase in its time period?

6. A particle is executing S H M of amplitude 4 cm and T = 4 sec. find the time taken by it to move from positive extreme position to half of its amplitude?

7. Two linear simple harmonic motions of equal amplitudes and angular frequency w and 2 w are impressed on a particle along axis X and Y respectively. If the initial phase difference between them is π/2, find the resultant path followed by the particle?

8. The acceleration due to gravity on the surface of moon is 1.7 m/s². What is the time period of simple pendulum on moon if its time period on the earth is 3.5s? 9. Using the correspondence of S. H. M. and uniform circular motion, find displacement, velocity, amplitude, time period and frequency of a particle executing SH.M?

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