Oscillation amplitudeWhat is the amplitude of the oscillation?

Click For Summary

Homework Help Overview

The discussion revolves around a physics problem involving a cart attached to a spring, focusing on the concepts of oscillation amplitude and energy conservation. The original poster presents a scenario where the cart is displaced from its equilibrium position and has an initial velocity, prompting questions about calculating the amplitude of oscillation and the speed at equilibrium.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of energy conservation principles, specifically the relationship between kinetic and potential energy in the context of oscillations. There are inquiries about the correctness of the initial equations and the approach to finding the amplitude.

Discussion Status

Some participants confirm the correctness of the initial equations and suggest balancing the total energy against the potential energy at maximum amplitude. There is a mention of calculations related to velocity at equilibrium and the amplitude, indicating that some productive direction has been provided.

Contextual Notes

Participants are operating under the constraints of a homework assignment, which may limit the extent of their explorations and the depth of their discussions. There is also a focus on ensuring the accuracy of calculations without providing definitive solutions.

kolua
Messages
69
Reaction score
3

Homework Statement


A 1.4-kg cart is attached to a horizontal spring for which the spring constant is 60 N/m . The system is set in motion when the cart is 0.27m from its equilibrium position, and the initial velocity is 2.6 m/s directed away from the equilibrium position.

A. What is the amplitude of the oscillation?
B. What is the speed of the cart at its equilibrium position?

Homework Equations


E=K+U

The Attempt at a Solution


U=½kΔx2 =½⋅60⋅0.272=2.187J
K=½mv2=½⋅1.4⋅2.62=4.732J
E=K+U=½mvf2

Is this the right way to proceed?
 
Physics news on Phys.org
Your first equations are correct and the K+U for E (the total energy at that point) is correct, but now you need to balance T against the U of the spring at the maximum amplitude of the oscillation.
 
kolua said:

Homework Statement


A 1.4-kg cart is attached to a horizontal spring for which the spring constant is 60 N/m . The system is set in motion when the cart is 0.27m from its equilibrium position, and the initial velocity is 2.6 m/s directed away from the equilibrium position.

A. What is the amplitude of the oscillation?
B. What is the speed of the cart at its equilibrium position?

Homework Equations


E=K+U

The Attempt at a Solution


U=½kΔx2 =½⋅60⋅0.272=2.187J
K=½mv2=½⋅1.4⋅2.62=4.732J
E=K+U=½mvf2

Is this the right way to proceed?
Yes, that will give you the answer to one part. What about the other?
 
haruspex said:
Yes, that will give you the answer to one part. What about the other?
the Velocity at the equilibrium would be, √(2(2.187+4.732)/1.4)=Ve=3.14m/s
then E=½mVe2=½kΔX2, this X here would be the amplitude. X=0.324
 
kolua said:
the Velocity at the equilibrium would be, √(2(2.187+4.732)/1.4)=Ve=3.14m/s
then E=½mVe2=½kΔX2, this X here would be the amplitude. X=0.324
Haven't checked the numbers in detail, but that looks right.
 

Similar threads

Replies
1
Views
1K
Replies
3
Views
953
Replies
13
Views
2K
Replies
1
Views
2K
Replies
9
Views
2K
  • · Replies 21 ·
Replies
21
Views
5K
  • · Replies 15 ·
Replies
15
Views
5K
Replies
1
Views
3K
  • · Replies 17 ·
Replies
17
Views
2K
Replies
3
Views
1K