Resonance

Question 1

What is the effect of constant force applied to an oscillating system?

Answer 1

The equilibrium position is moved

Question 2

If a harmonic force Fsin(Ωt) is applied, what is the displacement?

Answer 2

Xsin(Ωt-θ)

Question 3

What is the relationship between the amplitude of harmonic force and the amplitude of displacement?

Answer 3

X = (keff - meffΩ^2)^-1 * F

Question 4

What is the condition for resonance?

Answer 4

Ω = ωn

Question 5

What is the condition for “beats” (a short period oscillation which varies its amplitude sinusoidally)?

Answer 5

Ω ≈ ωn but not equal

Question 6

What is the steady state solution also known as?

Answer 6

The particular solution, the part which has frequency Ω

Question 7

What is the sum of the Homogeneous and Particular solutions?

Answer 7

The total solution

Question 8

How do you calculate the time period of free vibrations of a damped system?

Answer 8

T = 2 pi/omega d

Question 9

If a mass is placed onto a spring mass system as a step load, how does this affect the problem?

Answer 9

Oscillating mass = system mass + applied mass
Step load = applied mass * g

Question 10

What is the condition for static instability?

Answer 10

Spring force = kx
Force increases constantly over time

Question 11

What is the condition for dynamic instability?

Answer 11

Damping force = cx’
Force varies sinusoidally but amplitude increases over time