What is the displacement of a critically damped forced harmonic oscillator?

In summary, the conversation discusses a question about a 9 kg mass attached to a spring with a spring constant of 4 N/m. An external force of 10sin(3t) N is applied at time t=0, with a damping coefficient of 12 N-sec/m. The questions asked are: 1) to determine if the system is over damped, critically damped, or under damped, 2) to find the displacement y(t) of the mass at time t, and 3) to identify the transient solution and the steady state solution. The answer is that the system is critically damped and the displacement can be found by looking up "forced harmonic oscillator".
  • #1
Eggmans
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0
Spring Constant Question...please help!

Hello .I have an annoying question here...A 9 kg mass attached to a spring with spring constant 4 N/m. At time t=0 and external force F(t)=10sin(3t) N is applied to the mass. The damping coefficient for the system equals 12 N-sec/m.

NOTE: If y(t) represents the deviation at time t of the mass from the equilibrium position then y(0)=0 and y'(0)=01) Determine if the system is over damped, critically damped, or under damped

2) find the displacement y(t) of the mass at time t

3) Identify the transient solution and the steady state solutionI've stared at this for a while now and I have no idea what to do...I know it's critically damped but I can't figure out the displacement.
 
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  • #2


Look up "forced harmonic oscillator".
 

What is a spring constant?

A spring constant, also known as a force constant, is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a certain distance.

How is spring constant calculated?

Spring constant is calculated by dividing the force applied to the spring by the distance the spring is stretched or compressed. This is represented by the equation k = F/x, where k is the spring constant, F is the applied force, and x is the displacement of the spring.

What are the units of spring constant?

The units of spring constant depend on the units used for force and distance. In the SI system, the unit of spring constant is newtons per meter (N/m). In the English system, it is pounds per inch (lb/in).

Why is spring constant important?

Spring constant is important because it helps determine the behavior of a spring. It can be used to predict how much a spring will stretch or compress when a certain force is applied to it, and it is also used in many engineering applications.

How does temperature affect spring constant?

Temperature can affect spring constant by changing the stiffness of the material the spring is made of. As temperature increases, the atoms in the material vibrate more, causing the spring to become less stiff. This can result in a change in the spring constant and affect the behavior of the spring.

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