10.3.1 Damped Simple Harmonic Motion

Question 1

Damped Simple Harmonic Motion

Answer 1

• The differential equation describing damped simple harmonic motion is . Its solution (when b is small) is a cosine curve that dies away exponentially with time.
• Depending on the amount of friction present, a system can be either under damped, critically damped, or overdamped.
• The energy of a damped simple harmonic oscillator can be approximated by considering the amplitude of its motion.

Question 2

Which of the following conditions describes the case for light damping (underdamping)?

Answer 2

w ~~ w0

Question 3

Suppose a system has a damping force and the system’s equation of motion is given by F = -kx - bv. Which of the following is the unit of b

Answer 3

kg / s

Question 4

The solution of a damped oscillating system is given by x(t) = Ae^-bt/2m cos(wt + theta)
Which of the following is the position of the system at t = 0?

Answer 4

x(0) = A cos theta

Question 5

Shock absorbers in a car are designed to undergo which of the following types of damping?

Answer 5

critical damping

Question 6

The solution of a damped oscillating system with a drag force -bvis given by x(t) = Ae^-bt/m cos(wt + theta). There are four constant in this solution. Which two constants depend on the initial conditions of the system?

Answer 6

A and theta

Question 7

Consider an oscillating system with a damping force, Fd = -bv, where b is a constant. The equation of motion of the system is given by F = -kx-bv. Fd is a damping force only if b is positive

Answer 7

true

Question 8

In a damped oscillatory system, which of the following is the criterion for critical damping?

Answer 8

w0^2 = (b/2m)^2

Question 9

A damping force F = −bv resists the motion of an oscillating system. How is the amplitude affected as t increases?

Answer 9

A = 0

Question 10

How much time does it take for the energy to drop to 0.368 of its original value?

Answer 10

t = m/b s