10.3.2 Driven Oscillators

Question 1

Driven Oscillators

Answer 1

• By applying a driving force at an appropriate frequency, harmonic oscillations can be maintained in spite of frictional forces.
• The differential equation describing forced, damped harmonic motion is . Its steady-state solution is .
• When a driving force is applied to a system at the same frequency as the natural frequency, large oscillations result. This phenomenon is called resonance

Question 2

Which of the following is not an oscillatory driving force?

Answer 2

F0e^wt

Question 3

True or false?
Suppose the damping force in an oscillatory system increases while the mass, spring constant, and the driving frequency stay the same. This causes the amplitude to decrease. Even after damping increases, the system can be adjusted so that the amplitude doesn’t change.

Answer 3

true

Question 4

Suppose the driving frequency, spring constant, and mass of a system stay the same while the damping increases. How would the system respond?

Answer 4

The amplitude will decrease.

Question 5

A system with natural frequency w0 is driven with a frequency wd such that wd&raquo_space; w0. How does the amplitude of the oscillatory system respond?

Answer 5

A dies off steadily.

Question 6

Which of the following is the equation of motion for a driven oscillatory system? Assume there is no damping.

Answer 6

d^2x/dt^2 + k/m x = F0/m cos wdt

Question 7

A damped oscillatory system that is driven with frequency wd experiences resonance at which of the following frequencies?

Answer 7

wd = w0

Question 8

Which of the following indicates the amplitude if there is no damping in the system?

Answer 8

F0/m / (wd^2 - k/m)

Question 9

A system with natural frequency w0 is driven with a frequency wd. Which of the following is a possible solution for the equation of the system’s motion?

Answer 9

A cos(wd + theta)

Question 10

What happens tot he amplitude of the system if it is driven at the natural frequency?

Answer 10

A becomes infinite.