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

• ryley
In summary: Thanks for asking.Oh sure thing, Ill be home tomorrow and will upload the solutions I have! Thanks for asking.
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!

Last edited:
##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 said:
##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.

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
Delta2 said:
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!

ryley said:
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?
ryley said:
What is the frequency? mass of block? amplitude?.

ryley
SammyS said:
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!

## 1. Why is my thinking incorrect?

Your thinking may be incorrect due to a number of factors, such as bias, limited understanding of the subject, or lack of evidence to support your ideas. It is important to critically analyze your thoughts and seek out alternative perspectives to ensure accuracy.

## 2. How can a block and spring be driven by a motor?

A block and spring can be driven by a motor by attaching the spring to the block and then connecting the motor to the block. The motor's rotational force will cause the block to move, thus stretching and compressing the spring.

## 3. What is the purpose of using a motor to drive a block and spring?

The purpose of using a motor to drive a block and spring is to create a controlled and consistent motion. This can be useful in experiments and engineering applications where precise movements are needed.

## 4. How does the motor affect the motion of the block and spring?

The motor affects the motion of the block and spring by providing a source of external energy. The motor's rotational force transfers to the block, causing it to move and thus stretching and compressing the spring. The speed and direction of the motor can also impact the motion of the block and spring.

## 5. Are there any limitations to using a motor to drive a block and spring?

Yes, there are limitations to using a motor to drive a block and spring. The size and strength of the motor can limit the maximum force that can be applied to the block and spring. Additionally, the motor's speed and torque may affect the precision and control of the motion. Environmental factors such as friction and air resistance may also impact the motion of the block and spring.

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