Solve Disk & Coil Spring Motion: Get Amplitude Help

In summary: Can you fill in the details for this context?In summary, the equation states that if mass is added to the moving system, but not additional energy to do the work, how things must naturally change to adjust to the increased inertia and still move under the influence of the same elastic energy.
  • #1
Lil123
8
0
New user has been reminded to always show their work on schoolwork problems.
Homework Statement
A solid disk of mass M and Raduis R is on vertical .The shaft is
attached to a coil spring that exact a linear restoring torque of magnitude C theta where theta is the angle measured from the static equilibrium position in C is a constant neglect the mass of the shaft and the spring and assume the bearing to be frictionless.




1.Show that the disk and undergo simple harmonic motion motion and find the frequency frequency of the motion


2.Suppose that the disc is moving according to theta equals to theta not sin omega t where Omega is the frequency found in part a at time T1 equals to pi by Omega a ring of sticky putty of mass M and radius R is dropped cocentrically on the disc find the new amplitude of the motion
Relevant Equations
Li =Lf
I was able to solve part 1 but I am not
Screenshot_20230620-095315_Drive.jpg
not getting how to find new amplitude of the motion . Please help me
 
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  • #2
Lil123 said:
2.Suppose that the disc is moving according to theta equals to theta not sin omega t where Omega is the frequency found in part a at time T1 equals to pi by Omega a ring of sticky putty of mass M and radius R is dropped cocentrically on the disc find the new amplitude of the motion
Took me a while to decode that. Do you mean
"Suppose that the disc is moving according to ##\theta=\theta_0\sin (\omega t )## where ω is the frequency found in part 1.
"At time ##T_1 = \pi /\omega## a ring of sticky putty of mass M and radius R is dropped concentrically on the disc. Find the new amplitude of the motion."
?

For part 2, you need to show an attempt. You have quoted the relevant equation. Can you fill in the details for this context?
 
  • #3
This is the above question. How do I find new amplitude of the motion ?
 

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  • #4
Lil123 said:
This is the above question. How do I find new amplitude of the motion ?
Using your conservation of angular momentum equation.
What is the total angular momentum of the system just before the putty hits the disc? So what is the angular speed just after?
 
  • #5
haruspex said:
Using your conservation of angular momentum equation.
What is the total angular momentum of the system just before the putty hits the disc? So what is the angular speed just after?
Yes , but how do I find angular speed ? .I know angular frequency of the system before and after the putty hits the disc
 
  • #6
Lil123 said:
Yes , but how do I find angular speed ? .I know angular frequency of the system before and after the putty hits the disc
You can find the angular speed before the collision either from energy conservation or from the given equation of motion.
 
  • #7
Lil123 said:
...
2.Suppose that the disc is moving according to theta equals to theta not sin omega t where Omega is the frequency found in part a at time T1 equals to pi by Omega a ring of sticky putty of mass M and radius R is dropped cocentrically on the disc find the new amplitude of the motion
Relevant Equations: Li =Lf

I was able to solve part 1 but I am not View attachment 328105not getting how to find new amplitude of the motion . Please help me
If mass is added to the moving system, but not additional energy to do the work, how things must naturally change to adjust to the increased inertia and still move under the influence of the same elastic energy?

Please, see:
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
 
  • #8
Lnewqban said:
the same elastic energy?
Mechanical energy is not conserved here. @Lil123 quoted the relevant equation.
 
Last edited:

FAQ: Solve Disk & Coil Spring Motion: Get Amplitude Help

What is the basic principle behind the motion of a disk and coil spring system?

The motion of a disk and coil spring system is governed by Hooke's Law and Newton's laws of motion. Hooke's Law states that the force exerted by a spring is proportional to its displacement from its equilibrium position, F = -kx, where k is the spring constant and x is the displacement. Newton's second law, F = ma, relates the net force acting on the disk to its acceleration. The system typically exhibits simple harmonic motion, characterized by oscillations about an equilibrium position.

How do you determine the amplitude of oscillation in a disk and coil spring system?

The amplitude of oscillation is the maximum displacement of the disk from its equilibrium position. It can be determined by measuring the initial displacement when the disk is released from rest or by using energy conservation principles. The total mechanical energy in the system, which is the sum of kinetic and potential energy, remains constant. By equating the maximum potential energy (at maximum displacement) to the total energy, you can solve for the amplitude.

What factors affect the frequency of oscillation in a disk and coil spring system?

The frequency of oscillation depends on the mass of the disk (m) and the spring constant (k). It is given by the formula f = (1/2π)√(k/m). Thus, increasing the mass of the disk will decrease the frequency, while increasing the spring constant will increase the frequency. The frequency is independent of the amplitude of oscillation.

How can damping affect the motion of a disk and coil spring system?

Damping introduces a resistive force that opposes the motion of the disk, typically proportional to the velocity of the disk. This force reduces the amplitude of oscillation over time and can change the frequency of the system. In the presence of damping, the system may exhibit underdamped, critically damped, or overdamped behavior, depending on the damping coefficient. Underdamped systems still oscillate but with decreasing amplitude, critically damped systems return to equilibrium without oscillating, and overdamped systems return to equilibrium more slowly without oscillating.

Can you provide an example problem involving a disk and coil spring system and its solution?

Sure! Consider a disk of mass 0.5 kg attached to a spring with a spring constant of 200 N/m. The disk is displaced 0.1 m from its equilibrium position and released. Find the amplitude and the frequency of oscillation.First, the amplitude is given directly as the initial displacement, which is 0.1 m.To find the frequency, we use the formula f = (1/2π)√(k/m). Substituting the given values:f = (1/

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