Finding amplitude of oscillation with only k, x, v, and a

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Homework Help Overview

The problem involves an oscillating system characterized by a block attached to a string, with given parameters including spring constant k, position x, velocity v, and acceleration a. The objective is to find the amplitude of the motion without using energy considerations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to solve for the angular frequency using the relationship between acceleration and position but expresses uncertainty about how to handle the non-linear nature of the equations involving trigonometric functions. Some participants suggest substituting known values into the equations to create linear relationships, while others question the feasibility of eliminating variables due to the trigonometric components.

Discussion Status

The discussion is ongoing, with participants exploring different methods to manipulate the equations. Some guidance has been offered regarding treating trigonometric functions as separate variables, and a suggestion to use a trigonometric identity has been made. However, there is still a lack of consensus on how to proceed effectively.

Contextual Notes

The original poster notes the constraint of not using energy methods, which may limit the approaches available for solving the problem. There is also a mention of having two equations with three unknowns, indicating a potential challenge in finding a unique solution.

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Homework Statement


An oscillating system of a block attached to a string where k = 400 at some time t has a position x of 0.1 m, velocity of -13.6 m/s, and accel. of -123 m/s^2. Find the amplitude of the motion. Do not use energy.


Homework Equations


x = Acos(wt + phi)
v = -Awsin(wt + phi)
a = -Aw^2cos(wt + phi)

The Attempt at a Solution


I can solve for omega by using sqrt(-a / x), we still have 3 unknowns A, t, and phi. We have 3 equations, but they are not linear equations so I don't know how to solve them simultaneously. What other method is there that I can use since I can't use energy?
 
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Hi PhizKid! :smile:
PhizKid said:
x = Acos(wt + phi)
v = -Awsin(wt + phi)
a = -Aw^2cos(wt + phi)

substitute the given values for x v and a

then you have three linear equations …

start eliminating variables :wink:
 
But these are trig functions. Doesn't this make the equations non-linear? I'm not sure how to eliminate variables that have trig functions in them.
 
treat cos(wt + phi) and sin(wt + phi) as being variables in their own right! :smile:
 
This doesn't work. When I simplify the equations for x and a, they are both identical:

alpha = cos(wt + phi)
beta = sin(wt + phi)

0.100 = A * alpha
0.100 = A * alpha
0.388 = A * beta

So it's really 2 equations with 3 unknowns... :(
 
There is an identity relating sin and cos. Use it.
 

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