# Oscillations Multiple Choice Questions

Q1. Two-point masses of 3 Kg and 2 Kg are attached at the two ends of a horizontal spring with spring constant k=200 N/m. Find the natural frequency of vibration of the system.

1. 2.17 Hz
2. 2.05 Hz
3. 3.15 Hz
4. 1.9 Hz

Q2. A spring compressed by 0.2 m develops a restoring force of 10 N. A body of mass 5 Kg is placed on it. What would be the force constant k of the spring and the depression of the springy under the weight of the body?

1. 40 Nm-1, 0.5m
2. 50 Nm-1,0.5m
3. 0.5 Nm-1,0.5m
4. 60 Nm-1,0.5m

Q3. In simple harmonic motion, motion is executed by a particle that is subject to a force which is ___________to the displacement of the particle and is directed towards the______________.

1. proportional, extreme position
2. inversely proportional, mean position
3. proportional, mean position
4. inversely proportional, extreme position

Answer :- (3) proportional, mean position

Q4.Under what condition would the angular frequency ω’ of the damped oscillator be equivalent to angular velocity ω of the undamped oscillator?

1. Damping constant, b is small
2. Force applied is small
3. Velocity of oscillator is small
4. Damping constant ,b is large

Answer :- (1) Damping constant, b is small

Q5. A mass of 0.3 Kg is attached to the end of the spring. If another mass of 0.04 Kg is added to the end of the spring, it stretches by 12 cm more. What would be the period of vibration of the system if 0.04 kg mass is removed?

1. 2.1 s
2. 1.7 s
3. 2.2 s
4. 1.9 s

Q6. If the sign-in equation F=-kx is changed what would happen to the motion of the oscillating body?

1. Motion would be linearly accelerated motion
2. Body would come at rest
3. Motion would be oscillating accelerated
4. Body would slow down

Answer :- (1) Motion would be linearly accelerated motion

Q7. If a pendulum clock is making more vibrations per day so that it shows more time than the actual time then which of its part needs to be altered and how?

1. Weight of bob should be increased
2. Length of pendulum should be decreased
3. Weight of bob should be decreased
4. Length of pendulum should be increased

Answer :- (4) Length of pendulum should be increased

Q8. What determines the natural frequency of a body?

1. Mass and speed of the body
2. Elastic properties and dimensions of the body
3. Position of the body with respect to force applied
4. Oscillations in the body

Answer :- (2) Elastic properties and dimensions of the body

Q9.If the length of a second’s pendulum is increased thrice, what would be its time period?

1. 2.35s
2. 6.02s
3. 3.46s
4. 2.08s

Q10. A particle of mass 5 g is executing simple harmonic motion with an amplitude of 0.3 m and time period π/5 s. The maximum value of the force acting on the particle is

1. 5 N
2. 4 N
3. 0.5 N
4. 0.15 N

Q11. If the reference particle P moves in a uniform circular motion, its projection along the diameter of the circle executes

1. circular motion
2. motion along x axis
3. motion along y axis
4. Simple Harmonic motion

Answer :- (4) Simple Harmonic motion

Q12. The phenomenon of increase in amplitude when the driving force is close to the natural frequency of the oscillator is known as

1. Resonance
2. Accelerated Amplitude
3. Epoch
4. Dampening

Q13. Equation of a body in S.H.M is x = 5 cos (3πt + π/3). Its amplitude and velocity at t = 2 s would be

1. 40.97 m/s
2. -41.5 m/s
3. -40.79 m/s
4. 40.5 m/s

Q14. Due to what force a simple pendulum remains in simple harmonic motion?

1. mg sinθ, component of weight due to gravitational force
2. mg , weight
3. a, acceleration
4. y, displacement

Answer :- (1) mg sinθ, component of weight due to gravitational force

Q15. A spring with spring constant K is divided into x number of equal pieces. What would be the spring constant of one small piece of spring?

1. x/k
2. xK
3. kx
4. xK /(x+1)

Q16. A hollow sphere filled with water and one small hole at bottom is hung by a long thread and made to oscillates.  What would be the effect on the period of oscillations as water slowly flows out of the hole at bottom?

1. Keep on increasing
2. First increases then decreases
3. First decreases then increases
4. Keeps on decreasing

Answer :- (2) First increases then decreases

Q17. A second pendulum is mounted in a space shuttle. Its period of oscillation will decrease when rocket is

1. ascending up with uniform acceleration
2. descending down with uniform acceleration
3. moving in geostationary orbit
4. moving up with uniform velocity

Answer :- (1) ascending up with uniform acceleration

Q18. Find the amplitude of the S.H.M whose displacement y in cm is given by equation y = 3 sin157t + 4cos157t where t is time in seconds.

1. 50Hz
2. 20Hz
3. 40Hz
4. 25Hz

Q19. The amplitude of a simple harmonic oscillator is doubled; then period of oscillator would

1. Double
2. Remain same
3. Four times
4. Become half

Q20. Value of spring constant depends upon

1. Elastic properties of the spring
2. Length of spring
3. Number of turns
4. Mass attached to spring

Answer :- (1) Elastic properties of the spring

Q21. The work done by the string of a simple pendulum in S.H.M is

1. mg
2. equal to kinetic energy of the system
3. zero
4. equal to total energy of system

Q22. In the ideal case of zero dampings, the amplitude of simple harmonic motion at resonance is:

1. zero
2. infinite
3. varies from zero to infinite
4. cannot be said

Q23. The amplitude of an oscillator reduces to one-fourth of its initial value when it completes 200 oscillations. What will be its amplitude, when it completes 400 oscillations.

1. 1/16
2. 1/10
3. 4/16
4.   ½

Q24. The reason why oscillations becomes damped is _________

1. Normal force
2. Tangential force
3. Friction
4. Equidistant force

Q25. Epoch is measured in

2. Meters
3. gram/cm
4. seconds

Q26. A particle in S.H.M with frequency f. The frequency at which its kinetic energy changes into potential energy is

1. 3f
2. f/3
3. 4f
4. 2f

Q27. If the strong external periodic driving force matches one or more of the natural frequencies of the mechanical structure like bridge, aero plane, buildings then the resulting oscillations could

1. Move the structure
2. Cause echo in structure
3. Rupture /damage the structure
4. Would have no effect on structure

Answer :- (3) Rupture /damage the structure

Q28. On applying forced vibrations, the resonance wave becomes very fast when

1. Restoring force is big
2. Damping force is small
3. Applied periodic force is more
4. Oscillations are small

Answer :- (2) Applied periodic force is more

Q29. The motion of the simple pendulum is said to be S.H.M when its angle θ through which bob is displaced from its equilibrium position is

1. θ is very large
2. θ is zero
3. θ is very small
4. θ = cosθ

Answer :- (3) θ is very small

Q30. Particle with amplitude A, displacement Y and time period T starts in SHM from its mean position. What would be particle’s displacement when its speed is half of the maximum speed?

1. 3A/5
2. √3 A/2
3. √2 A/3
4. A/√3

Q31. Energy is supplied to the damped oscillatory system at the same rate at which it is dissipating energy, then the amplitude of such oscillations would become constant. Such oscillations are called

1. Undamped oscillations
2. Maintained oscillations
3. Coupled oscillations
4. Damped oscillations

Q32. At what distance from the mean position would the K.E of a particle in simple harmonic motion be equal to its potential energy?

1. a√2
2. 2√a
3. a
4. a/2

Q33. A simple pendulum with length l and bob of mass m is executing S.H.M of small amplitude a. The expression for maximum tension in the string will be

1. mg [1+ (a2/l2)]
2. mg[1+(a/l)
3. mg
4. mg [1+(a/l)]2

Answer :- (1) mg [1+ (a2/l2)]

Q34. Which is a necessary and sufficient condition for simple harmonic motion?

1. Constant speed
2. Proportionality between force and displacement from mean position
3. Proportionality between acceleration and displacement
4. Proportionality between restoring force and displacement from equilibrium position

Q35. Under forced oscillation, the phase of the harmonic motion of the particle and phase of driving force

1. Are same
2. Are different
3. Both are zero
4. Not present

Q36. The amplitude of S.H.M at resonance is _______ in the ideal case of zero damping.

1. Maximum
2. Zero
3. Minimum
4. Infinite

Q37. The equation of motion of a particle is x = 3 cos(0.45 t + π/4) m. Its maximum acceleration is

1. 0.50 ms-2
2. 0.60 ms-2
3. 0.55 ms-2
4. 0.45 ms-2

Q38. If we triple the mass on a simple pendulum, the frequency will be__________

1. Three times what it was.
2. Six times what it was.
3. Remain same
4. One-third what it was.

Q39. What is the maximum Kinetic energy and minimum potential energy of a harmonic oscillator with amplitude 0.03 m? Force constant is 4 x 105 N/m and total mechanical energy is 230 J.

1. 200J, 40J
2. 190J, 60J
3. 180J,50J
4. 210J,60J

Q40. A frequency of 1 Hz corresponds to:

1. 2 vibrations per second
2. a time period of ½ second
3. 10 vibrations per second
4. 1 vibration per second

Answer :- (4) 1 vibration per second