Question 1

In a forced oscillation, after the steady state is reached, the system oscillates with the:

Accepted Answer

Frequency of the applied periodic force. Transients at the natural frequency die out because of damping, leaving the system oscillating at the driving frequency.

Question 2

Resonance in a forced oscillation occurs when the frequency of the driving force is:

Accepted Answer

Equal to the natural frequency of the system. At this match, energy is fed into the system in step with its own motion each cycle, producing the largest possible amplitude.

Question 3

At resonance, the amplitude of a forced oscillation is:

Accepted Answer

Maximum. The driving force works with the motion throughout each cycle, so the energy transfer per cycle is maximum and the amplitude peaks.

Question 4

Increasing the damping of a resonant system has the effect of:

Accepted Answer

Reducing the amplitude at resonance and broadening the resonance curve. Damping limits the maximum amplitude and makes the response less sharply peaked, so the system responds over a wider band of frequencies.

Question 5

In the ideal case of zero damping, the amplitude of a system driven exactly at resonance would:

Accepted Answer

Grow without limit. With nothing to dissipate the energy fed in each cycle, the amplitude would in principle increase indefinitely. Real systems always have some damping.

Question 6

Soldiers are ordered to break step while marching across a suspension bridge because:

Accepted Answer

Their rhythmic steps might resonate with a natural frequency of the bridge. A periodic driving force matching a natural frequency of the structure could build up dangerously large oscillations through resonance.

Question 7

The sharpness of resonance of an oscillating system is greatest when the damping is:

Accepted Answer

Very small. Low damping gives a tall, narrow resonance peak, meaning the system responds strongly only very close to its natural frequency.

Question 8

Tuning a radio receiver to a particular station is an everyday example of:

Accepted Answer

Electrical resonance. The tuning knob adjusts a capacitance so that the circuit's natural frequency matches the carrier frequency of the desired station, which is then amplified far more than the rest.

Question 9

The natural frequency of an oscillating system depends on:

Accepted Answer

The physical properties of the system, such as its mass and stiffness. For a spring-mass system f_0 = \dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}} — a property of the system alone, independent of how it is driven.

Question 10

A child on a swing is pushed gently once every cycle at just the right moment, making the swing rise higher and higher. This illustrates:

Accepted Answer

Resonance. The pushes are applied at the swing's natural frequency and in phase with its motion, so each push adds energy and the amplitude grows.

Question 11

A freely vibrating system loses energy to its surroundings, but a system in a steady forced oscillation maintains a constant amplitude because:

Accepted Answer

The driving force supplies exactly the energy lost to damping in each cycle. Steady state is a balance: energy input per cycle from the driver equals energy dissipated per cycle by damping.

Question 12

The collapse of the Tacoma Narrows bridge in 1940 is commonly cited as an example of the destructive effect of:

Accepted Answer

Resonant build-up of oscillations driven by the wind. Periodic forcing from the wind matched a natural torsional mode of the deck, and the oscillations grew until the structure failed.

Question 13

In Melde's experiment, standing waves of large amplitude appear on a string when:

Accepted Answer

The frequency of the tuning fork matches a natural frequency of the string. The experiment demonstrates resonance: adjusting the length or tension until a natural frequency of the string equals the driving frequency produces large, stable loops.

Question 14

A tuning fork held over a tube of adjustable air column produces a loud sound at certain lengths. This is because:

Accepted Answer

The air column resonates when its natural frequency equals the fork frequency. At the resonant lengths a standing wave is set up in the air column, and the amplitude of vibration — and hence the loudness — becomes large.

Question 15

A forced oscillation differs from a free oscillation chiefly because a forced oscillation:

Accepted Answer

Is maintained by an external periodic force. A free oscillation happens at the system's own frequency after an initial disturbance; a forced oscillation is continuously driven from outside.

Question 16

When the driving frequency is very much greater than the natural frequency of a system, the amplitude of the forced oscillation is:

Accepted Answer

Very small. The system's inertia prevents it from following such rapid forcing, so it barely responds and the amplitude falls well below the resonant value.

Question 17

A mass of 1	ext{ kg} on a spring of force constant 400	ext{ N/m} has a natural frequency of approximately:

Accepted Answer

3.18	ext{ Hz}. \omega_0 = \sqrt{\dfrac{k}{m}} = \sqrt{400} = 20	ext{ rad/s}, so f_0 = \dfrac{20}{2\pi} \approx 3.18	ext{ Hz}.

Question 18

A mass of 0.25	ext{ kg} hangs from a spring of force constant 100	ext{ N/m}. Resonance occurs when the driving angular frequency is:

Accepted Answer

20	ext{ rad/s}. Resonance requires the driving frequency to match the natural one: \omega_0 = \sqrt{\dfrac{k}{m}} = \sqrt{\dfrac{100}{0.25}} = \sqrt{400} = 20	ext{ rad/s}.

Question 19

A simple pendulum of length 1	ext{ m} has a natural frequency of approximately (g = 10	ext{ m/s}^2):

Accepted Answer

0.50	ext{ Hz}. \omega_0 = \sqrt{\dfrac{g}{L}} = \sqrt{10} = 3.16	ext{ rad/s}, so f_0 = \dfrac{3.16}{6.283} \approx 0.50	ext{ Hz}.

Question 20

A mass-spring system has a natural period of 0.5	ext{ s}. The driving frequency that produces resonance is:

Accepted Answer

2	ext{ Hz}. Resonance occurs when the driving frequency equals the natural frequency f_0 = \dfrac{1}{T} = \dfrac{1}{0.5} = 2	ext{ Hz}.

Forced Oscillations & Resonance — MH-CET Physics MCQs with Solutions

Questions with solutions