P.3.6.1.4 Forced vibrations and resonance

A metal panel is driven to vibrate at different frequencies. The amplitude a of the vibration is measured at each frequency. The graph shows the variation of amplitude with driven frequency.

The damping of the metal panel is increased without changing the mass of the panel. Which graph shows the variation of a with frequency with increased damping?

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A mechanical oscillator is set into motion by a periodic driving force whose frequency is steadily increased from a low value.

What is correct for this system?

• Forced vibrations occur only at particular frequencies.

• The oscillator is subject to damping only at the resonant frequency.

• When resonance occurs the damping force is a minimum.

• The oscillator will not continue to resonate when the periodic driving force is removed.

The diagram shows a string XY supporting a heavy pendulum P and four pendulums A, B, C and D of smaller mass.

Pendulum P is set in oscillation perpendicular to the plane of the diagram.

Which one of the pendulums, A to D, then oscillates with the largest amplitude?

• A

• B

• C

• D

A periodic force is applied to a lightly-damped object causing the object to oscillate.

The graph shows how the amplitude A of the oscillations varies with the frequency f of the periodic force.

Which one of the following statements best describes how the shape of the curve would differ if the damping had been greater?

• the curve would be lower at all frequencies

• the curve would be higher at all frequencies

• the curve would be unchanged except at frequencies above the resonant frequency where it would be lowe

• the curve would be unchanged except at frequencies above the resonant frequency where it would be higher

An oscillatory system, subject to damping, is set into vibration by a periodic driving force of frequency f. The graphs, A to D, which are to the same scale, show how the amplitude of vibration A of the system might vary with f, for various degrees of damping.

Which graph best shows the lightest damping?

• A

• B

• C

• D

A mechanical system is oscillating at resonance with a constant amplitude. Which one of the following statements is not correct?

• The applied force prevents the amplitude from becoming too large.

• The frequency of the applied force is the same as the natural frequency of oscillation of the system.

• The total energy of the system is constant.

• The amplitude of oscillations depends on the amount of damping.

Which one of the following statements always applies to a damping force acting on a vibrating system?

• It is in the same direction as the acceleration.

• It is in the same direction as the displacement.

• It is in the opposite direction to the velocity.

• It is proportional to the displacement.

Which one of the following statements concerning forced vibrations and resonance is correct?

• An oscillating body that is not resonating will return to its natural frequency when the forcing vibration is removed.

• At resonance, the displacement of the oscillating body is 180° out of phase with the forcing vibration.

• A pendulum with a dense bob is more heavily damped than one with a less dense bob of the same size.

• Resonance can only occur in mechanical systems.

Which one of the following statements always applies to a damping force acting on a vibrating system?

• It is in the same direction as the acceleration.

• It is in the opposite direction to the velocity.

• It is in the same direction as the displacement.

• It is proportional to the displacement.

Which one of the following statements about an oscillating mechanical system at resonance, when it oscillates with a constant amplitude, is not correct?

• The amplitude of oscillations depends on the amount of damping.

• The frequency of the applied force is the same as the natural frequency of oscillation of the system.

• The total energy of the system is constant

• The applied force prevents the amplitude from becoming too large.