BITSAT Physics Oscillations MCQs

Question: The following figure depict a circular motion. The radius of the circle, the period of revolution, the initial position and the sense of revolution are indicated on the figure.

 The simple harmonic motion of the x-projection of the radius vector of the rotating particle P can be shown as

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

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)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A 1 kg mass is attached to a spring of force constant 600 N/m and rests on a smooth horizontal surface with other end of the spring tied to wall as shown in figure. A second mass of 0.5 kg slides along the surface towards the first at 3m/s. If the masses make a perfectly inelastic collision, then find amplitude and time period of oscillation of combined mass

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Vertical displacement of a Planck with a body of mass m on it is varying according to law y = sin ωt +√3 cosωt. The minimum value of ω for which the mass just breaks off the Planck and the moment it occurs first after t = 0, are given by

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A load of mass m falls from a height h on to the scale pan hung from the spring as shown in the figure. If the spring constant is k and mass of the scale pan is zero and the mass m does not bounce relative to the pan, then the amplitude of vibration is

• a) mg/d
• b)

  

• c)

  

• d)

  

Answer:

Question: The displacement of a particle is given at time t, by: x = Asin(-2ωt) + B sin² ωt. Then

• a) the motion of the particle is SHM with an amplitude of 
• b) the motion of the particle is not SHM, but oscillatory with a time period of T = π/ω
• c) the motion of the particle is oscillatory with a time period of T = π/2ω
• d) the motion of the particle is a periodic

Answer: the motion of the particle is SHM with an amplitude of 

Question: Two particles P and Q describe S.H.M. of same amplitude a, same frequency f along the same straight line. The maximum distance between the two particles is a √2. The initial phase difference between the particle is –

• a) zero
• b) π/2
• c) π/6
• d) π/3

Answer: π/2

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: 84.6 minutes

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: π/4 ω 

Question: One end of a long metallic wire of length L tied to the ceiling. The other end is tied with a mass less spring of spring constant K. A mass hangs freely from the free end of the spring. The area of cross section and the young’s modulus of the wire are A and Y respectively. If the mass slightly pulled down and released, it will oscillate with a time period T equal to :

• a) 2π √(m/ K)
• b) 2π √m(YA+KL) / (YAK)
• c) 2π √(mYA / KL)
• d) 2π √(mL / YA)

Answer: 2π √m(YA+KL) / (YAK)

Question: Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants?

• a) a + bx – cx²
• b) bx²
• c) a – bx + cx²
• d) – bx

Answer: – bx

Question: A mass m is suspended from a spring of force constant k and just touches another identical spring fixed to the floor as shown in the figure. The time period of small oscillations is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

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

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: In case of a forced vibration, the resonance wave becomes very sharp when the

• a) Restoring force is small
• b) Applied periodic force is small
• c) Quality factor is small
• d) Damping force is small

Answer: Damping force is small

Question: A pendulum bob carries a +ve charge +q. A positive charge +q is held at the point of support. Then the time period of the bob is –

• a) greater than 2π √L / g
• b) less than 2π √L / g
• c) equal to 2π √L / g
• d) equal to 2π √2L / g

Answer: greater than 2π √L / g

Question: Two oscillating systems; a simple pendulum and a vertical spring-mass-system have same time period of motion on the surface of the Earth. If both are taken to the moon, then–

• a) Time period of the simple pendulum will be more than that of the spring-mass system.
• b) Time period of the simple pendulum will be equal is that is of the spring-mass system.
• c) Time period of the simple pendulum will be less than of the spring-mass system
• d) Nothing can be said definitely without observation

Answer: Time period of the simple pendulum will be more than that of the spring-mass system.

Question: One end of a spring of force constant k is fixed to a vertical wall and other to a body of mass m resting on a smooth horizontal surface there is another wall at a distance x₀ from the body. The spring is then compressed by 2_x0 and released. The time taken to strike the wall is :

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The potential energy of a particle (U_x) executing S.H.M. is given by

• a) 

  

• b)

  

• c) 
• d)  U_x = a constant

Answer:

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: Decrease

Question: The height of liquid column in a U tube is 0.3 meter. If the liquid in one of the limbs is depressed and then released, then the time period of liquid column will be-

• a) 0.11 sec
• b) 19 sec
• c) 1.1 sec
• d) 2 sec

Answer: 1.1 sec