- #1
vxr
- 25
- 2
- Homework Statement
- One block of mass ##m = 0.20 kg## traveling at velocity ##v = 5 m/s## collides elastically with a second block of mass ##M = 0.80 kg## resting on a frictionless surface and connected to a spring with elastic force constant ##k = 80 N/m##.
What is the angular velocity ##\omega##, period ##T##, and the amplitude ##A## of block’s oscillations? Determine the respective values for the case when damping effects will appear with overall damping coefficient ##\beta = 21/s##.
- Relevant Equations
- ##\omega = \sqrt{\omega_{0}^2 - \beta^2}##
I saw this general formula:
##w_{0} = \sqrt{\frac{k}{m}}##
In my case both masses after collision create connected system, so ##w_{0} = \sqrt{\frac{k}{m+M}}##
Plugging it into ##\omega = \sqrt{\omega_{0}^2 - \beta^2}## gives :
##\omega = \sqrt{\frac{k}{m+M} - \beta^2} = \sqrt{80 - 21^2} < 0##
It's a root of negative value. Why is that happening? Am I doing something wrong, or perhaps the damping coefficient is relatively too large in this task?
One more question: I know how to calculate the period ##T##, but what about amplitude ##A##? Is it simply: ##A = A_{0}e^{-\beta t} \quad \land \quad A_{0} = 0 \Longrightarrow A = 0##? If this is the case, why is this ##A_{0} = 0## true?
##w_{0} = \sqrt{\frac{k}{m}}##
In my case both masses after collision create connected system, so ##w_{0} = \sqrt{\frac{k}{m+M}}##
Plugging it into ##\omega = \sqrt{\omega_{0}^2 - \beta^2}## gives :
##\omega = \sqrt{\frac{k}{m+M} - \beta^2} = \sqrt{80 - 21^2} < 0##
It's a root of negative value. Why is that happening? Am I doing something wrong, or perhaps the damping coefficient is relatively too large in this task?
One more question: I know how to calculate the period ##T##, but what about amplitude ##A##? Is it simply: ##A = A_{0}e^{-\beta t} \quad \land \quad A_{0} = 0 \Longrightarrow A = 0##? If this is the case, why is this ##A_{0} = 0## true?