Understanding Forced Motion in Driven Oscillators

1. A high-Q oscillator tends to ring (keep vibrating) for a longer time after being disturbed.

True

False

Low damping means slow energy loss, producing long-lasting oscillations after the driving force is removed.

Explanation

Low damping means slow energy loss, producing long-lasting oscillations after the driving force is removed.

2. Which statement is most accurate?

Resonance always destroys the system

Resonance can be useful or harmful depending on context and amplitude

Resonance only happens in sound

Resonance requires zero damping

Resonance can be beneficial in instruments and filters but harmful to structures if uncontrolled; damping affects response size but doesn't need to be zero.

Explanation

Resonance can be beneficial in instruments and filters but harmful to structures if uncontrolled; damping affects response size but doesn't need to be zero.

3. A system can resonate even if the driving force is small, provided damping is low and driving is near the natural frequency.

True

False

Efficient timing allows energy to accumulate over many cycles; low damping prevents rapid loss, enabling large steady amplitudes from small inputs.

Explanation

Efficient timing allows energy to accumulate over many cycles; low damping prevents rapid loss, enabling large steady amplitudes from small inputs.

4. Why are shock absorbers designed with high damping?

To amplify resonance

To reduce oscillations quickly and avoid resonance build-up

To increase Q

To make cars bounce more

High damping dissipates energy and prevents large oscillations, improving ride comfort and safety.

Explanation

High damping dissipates energy and prevents large oscillations, improving ride comfort and safety.

5. The 'sharpness' of resonance is often related to the ratio of resonant frequency to ______.

A narrower bandwidth means greater selectivity and higher Q, linking Q to peak sharpness.

Explanation

A narrower bandwidth means greater selectivity and higher Q, linking Q to peak sharpness.

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6. Increasing damping typically reduces the maximum amplitude at resonance.

True

False

More damping removes energy faster, preventing the driver from building as large an amplitude before losses balance input.

Explanation

More damping removes energy faster, preventing the driver from building as large an amplitude before losses balance input.

7. A strong sign of resonance in a response graph is:

A flat line everywhere

A clear peak at a particular frequency

Only negative values

No dependence on frequency

Resonance produces a maximum response at a specific frequency, reflecting the system’s natural tendency to oscillate.

Explanation

Resonance produces a maximum response at a specific frequency, reflecting the system’s natural tendency to oscillate.

8. Resonance can occur in electrical circuits as well as mechanical systems.

True

False

Resonance is general; any system that stores and exchanges energy between two forms can resonate.

Explanation

Resonance is general; any system that stores and exchanges energy between two forms can resonate.

9. If a resonant frequency shifts when you add mass to a system, that indicates the natural frequency depends on:

Only colour

System parameters like mass and stiffness

Only temperature

Only volume

Natural frequency is determined by physical parameters; changing mass or stiffness changes the resonant frequency.

Explanation

Natural frequency is determined by physical parameters; changing mass or stiffness changes the resonant frequency.

10. Which device is designed to have a high Q (sharp resonance)?

Car shock absorber

Tuning fork

Door closer mechanism

Sponge in water

Tuning forks vibrate for a long time and have a sharp frequency, while shock absorbers are designed to be heavily damped (low Q).

Explanation

Tuning forks vibrate for a long time and have a sharp frequency, while shock absorbers are designed to be heavily damped (low Q).

11. The resonance curve of a driven oscillator is a graph of:

Temperature vs time

Amplitude vs driving frequency

Mass vs volume

Pressure vs area

The resonance curve shows how a driven oscillator responds differently at different driving frequencies, with a peak near the natural frequency.

Explanation

The resonance curve shows how a driven oscillator responds differently at different driving frequencies, with a peak near the natural frequency.

12. Resonance amplitude stops growing when power input equals power lost to ______.

In steady-state, the driver supplies energy each cycle and damping removes it; amplitude stabilizes when these balance.

Explanation

In steady-state, the driver supplies energy each cycle and damping removes it; amplitude stabilizes when these balance.

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13. Which statement best matches 'steady-state response'?

The initial transient motion right after you start driving

The long-term oscillation after transients die out

Motion with zero frequency

Motion with no damping

After driving begins, the system settles into steady-state determined mainly by the driving frequency and damping.

Explanation

After driving begins, the system settles into steady-state determined mainly by the driving frequency and damping.

14. The phase difference between the driving force and the motion changes as you sweep through resonance.

True

False

Below resonance, the oscillator tends to follow the drive more closely; above resonance, it lags differently, with significant phase changes near the peak.

Explanation

Below resonance, the oscillator tends to follow the drive more closely; above resonance, it lags differently, with significant phase changes near the peak.

15. At resonance, the driving force is most effective because it is timed to:

Always oppose the motion

Add energy at the right phase of the motion

Stop the oscillator

Change the mass

Energy transfer depends on the relative phase between force and velocity; near resonance, the timing aligns for efficient energy transfer.

Explanation

Energy transfer depends on the relative phase between force and velocity; near resonance, the timing aligns for efficient energy transfer.

16. The quality factor (Q) is qualitatively higher when:

Damping is higher

Damping is lower

Frequency is zero

Mass is zero

Higher Q means less energy lost per cycle relative to energy stored, corresponding to lower damping and a sharper resonance.

Explanation

Higher Q means less energy lost per cycle relative to energy stored, corresponding to lower damping and a sharper resonance.

17. A lightly damped system usually has a narrow bandwidth (sharp resonance).

True

False

Low damping means energy stays stored in the oscillator for many cycles, producing a sharp peak with narrow bandwidth.

Explanation

Low damping means energy stays stored in the oscillator for many cycles, producing a sharp peak with narrow bandwidth.

18. The width of the resonance peak is often described by the ______ (frequency range around the peak).

Bandwidth indicates how selective the oscillator is to frequency; narrow bandwidth means strong selectivity near resonance.

Explanation

Bandwidth indicates how selective the oscillator is to frequency; narrow bandwidth means strong selectivity near resonance.

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19. Increasing damping typically makes the resonance peak:

Taller and narrower

Shorter and broader

Taller and broader

Unchanged

More damping increases energy loss per cycle, reducing maximum amplitude and widening the frequency range of noticeable response.

Explanation

More damping increases energy loss per cycle, reducing maximum amplitude and widening the frequency range of noticeable response.

20. The peak of the resonance curve occurs near the natural frequency of the system.

True

False

Maximum steady amplitude occurs when the driving frequency matches the natural frequency, which is the resonance condition.

Explanation

Maximum steady amplitude occurs when the driving frequency matches the natural frequency, which is the resonance condition.

Driven Oscillator Quiz: Test Your Knowledge Of Forced Motion

1. A high-Q oscillator tends to ring (keep vibrating) for a longer time after being disturbed.

2.

What first name or nickname would you like us to use?

2. Which statement is most accurate?

3. A system can resonate even if the driving force is small, provided damping is low and driving is near the natural frequency.

4. Why are shock absorbers designed with high damping?

5. The 'sharpness' of resonance is often related to the ratio of resonant frequency to ______.

6. Increasing damping typically reduces the maximum amplitude at resonance.

7. A strong sign of resonance in a response graph is:

8. Resonance can occur in electrical circuits as well as mechanical systems.

9. If a resonant frequency shifts when you add mass to a system, that indicates the natural frequency depends on:

10. Which device is designed to have a high Q (sharp resonance)?

11. The resonance curve of a driven oscillator is a graph of:

12. Resonance amplitude stops growing when power input equals power lost to ______.

13. Which statement best matches 'steady-state response'?

14. The phase difference between the driving force and the motion changes as you sweep through resonance.

15. At resonance, the driving force is most effective because it is timed to:

16. The quality factor (Q) is qualitatively higher when:

17. A lightly damped system usually has a narrow bandwidth (sharp resonance).

18. The width of the resonance peak is often described by the ______ (frequency range around the peak).

19. Increasing damping typically makes the resonance peak:

20. The peak of the resonance curve occurs near the natural frequency of the system.