Why is my thinking incorrect? -- Block and spring driven by a motor

[ryley]

Homework Statement

An oscillator consists of a block attached to a spring (k=400n/m). At some time t, the position (from equilibrium), velocity, and acceleration of the block are x= .100m, v= -13.6m/s, a= -123m/s^2.
What is the frequency? mass of block? amplitude.

Homework Equations

position function, velocity function, acceleration function

3.The attempt at a solution
The problem I'm having with this question is with part a. I understand the solution I looked up but what I don't understand is why I can solve for ω by rearranging v=ωx for ω=v/x? I know to use the acceleration formula a=(-ω^2)x and ω=√(a/x).
Is it that the velocity mentioned in the question is not the same form of velocity used in the velocity formula for SHM?

Any help would be much appreciated!

 

[Delta2]

##v(t)=\omega x(t)## is not true for all times t. It is true only as an equation between amplitudes that is ##v_0=\omega x_0##
On the other hand, ##a(t)=-\omega^2 x(t)## is true for all times t. So that's the equation to use to find ##\omega## since our data for x, v, and a are at some random time t.

 

[ryley]

Thanks for the response! I guess what I'm still confused about though is that an object that is oscillating has a velocity and acceleration value that are always changing depending on time. So if at some time t acceleration is 123m/s^2 at another time it would be different as well so I don't understand how we can assume acceleration in this problem is true at all times.

 

[ryley]

##v(t)=\omega x(t)## is not true for all times t. It is true only as an equation between amplitudes that is ##v_0=\omega x_0##
On the other hand, ##a(t)=-\omega^2 x(t)## is true for all times t. So that's the equation to use to find ##\omega## since our data for x, v, and a are at some random time t.

Thanks for the response! I guess what I'm still confused about though is that an object that is oscillating has a velocity and acceleration value that are always changing depending on time. So if at some time t acceleration is 123m/s^2 at another time it would be different as well so I don't understand how we can assume acceleration in this problem is true at all times.

 

[Delta2]

I didn't mean that acceleration is constant at all times, I meant that this equation
##a(t)=-\omega^2x(t)## is true at all times, this equation involves ##a(t)## and ##x(t)## as functions of time t, so they change when time t changes.

 

[ryley]

I didn't mean that acceleration is constant at all times, I meant that this equation
##a(t)=-\omega^2x(t)## is true at all times, this equation involves ##a(t)## and ##x(t)## as functions of time t, so they change when time t changes.

Oh okay that makes more sense! Thanks so much again!

 

[SammyS]

Oh okay that makes more sense! Thanks so much again!

Hello @ryley .
A belated ...

As a Homework Helper, it's good to see the final results/solutions obtained by those we help. After all, we are volunteers and receive no pay for the help we give.

What are the results you got for the questions you were to answer?

What is the frequency? mass of block? amplitude?.

 

[ryley]

Hello @ryley .
A belated ...

As a Homework Helper, it's good to see the final results/solutions obtained by those we help. After all, we are volunteers and receive no pay for the help we give.

What are the results you got for the questions you were to answer?

Oh sure thing, Ill be home tomorrow and will upload the solutions I have!