Spring Constant and Motion Analysis

The video tutorial explains the concept of free undamped motion using a mass-spring system. It begins by setting up the problem with initial conditions and derives a second-order linear homogeneous differential equation. The solution involves solving the characteristic equation to find complex solutions, leading to a general solution. Initial conditions are used to determine constants, and the spring constant K is calculated to ensure the mass does not exceed a displacement of 3 meters. The tutorial concludes with a graphical verification of the solution.

What is the initial velocity of the mass at time T equals zero?

• 3 meters per second

• 2 meters per second

• 1 meter per second

• 0 meters per second

Which equation represents the system of free undamped motion?

• m x double prime divided by KX equals zero

• m x double prime minus KX equals zero

• m x double prime plus KX equals zero

• m x double prime times KX equals zero

What form does the general solution of the differential equation take?

• X of T equals a times cosine of Omega t

• X of T equals a times sine of Omega t

• X of T equals a times sine of Omega t plus b times cosine of Omega T

• X of T equals a times cosine of Omega t plus b times sine of Omega T

What is the value of 'a' when using the initial condition X of zero equals zero?

• a equals three

• a equals two

• a equals one

• a equals zero

What is the amplitude of the sine function if the mass goes exactly three meters from the rest position?

• Two

• One

• Four

• Three

What is the value of the spring constant K for the mass to travel exactly three meters from the rest position?

• Two

• One

• Eight ninths

• One half

If the spring constant is greater than eight ninths, what happens to the mass?

• It does not move

• It travels less than three meters from the rest position

• It travels exactly three meters from the rest position

• It travels more than three meters from the rest position

What does the graph of X of T equals negative three sine of two-thirds T show?

• The mass travels more than three meters

• The mass travels less than three meters

• The mass travels exactly three meters

• The mass does not move

What happens to the mass when the spring constant is exactly eight ninths?

• It travels more than three meters

• It travels exactly three meters

• It does not move

• It travels less than three meters

What is the significance of the spring constant being greater than or equal to eight ninths?

• The mass will not move

• The mass will travel more than three meters

• The mass will not go further than three meters

• The mass will travel exactly three meters