Frequency of Oscillation of a Block & Spring

[QuantumKnight]

Homework Statement

An oscillator consists of a block attached to a spring (k=400 N/m). At some time t, the position, velocity, and accelleration of the block are x = 0.100m, v = -13.6 m/s, a - 123 m/s²

A) Calculate the frequency of the oscillation for the system
B)What is the mass of the block
C) What is the amplitue of the block motion?

Homework Equations

x(t) = Acos (wt + psi)

The Attempt at a Solution

I have tried to use the equation for Simple Harmonic Motion for position and then take the derivaties to find velocity and acceleration. I am still not understanding the phase shifts. I am not worried about B as I can find the mass thanks to the assistance earlier. Just a little guiadance as to what i need to look for in setting up this problem

 

[Orodruin]

Hint: You do not need to worry about the phase shift in order to solve (A) - assuming that x is measured relative to the equilibrium position.

 

[QuantumKnight]

For some reason the only equation I can think of to find frequency is 1/T. But this can't be right because I need to know the mass of the block. I can't use T = 2pi/w (w being omeaga) because I wasn't given an angular velocity. I know this is simple but I can't wrap my head around what I am missing.

 

[Orodruin]

How are acceleration, velocity, and displacement related? What expressions do you obtain for them?

 

[lep11]

For some reason the only equation I can think of to find frequency is 1/T. But this can't be right because I need to know the mass of the block. I can't use T = 2pi/w (w being omeaga) because I wasn't given an angular velocity. I know this is simple but I can't wrap my head around what I am missing.

Hello. Draw a free body diagram of the block at time t. Then you will easily figure out the net force and you already know the acceleration so actually you could begin by solving the mass of the block using Newtons 2nd law. You know how to calculate the frequency when you know m and k.However it is not said in the problem statement whether the block is oscillating vertically or horizontally. I think the other way would be to derive formulas for velocity and acceleration and you would end up having three equations and three unknows.

 

[Orodruin]

Hello. Draw a free body diagram of the block at time t. Then you will easily figure out the net force and you already know the acceleration so actually you could begin by solving the mass of the block using Newtons 2nd law. You know how to calculate the frequency when you know m and k.However it is not said in the problem statement whether the block is oscillating vertically or horizontally. I think the other way would be to derive formulas for velocity and acceleration and you would end up having three equations and three unknows.

This is actually the long way around. In order to solve (A), it does not matter what the spring constant is (assuming the mass is chosen such that the data are fulfilled).

 

[lep11]

This is actually the long way around. In order to solve (A), it does not matter what the spring constant is (assuming the mass is chosen such that the data are fulfilled).

Which one is the longer way?

 

[Orodruin]

To start by solving for the mass when you are a priori interested in the frequency. You do not need to include the information of the spring constant in order to find it, it is strictly only relevant for finding the mass in part (B).

 

[lep11]

To start by solving for the mass when you are a priori interested in the frequency. You do not need to include the information of the spring constant in order to find it, it is strictly only relevant for finding the mass in part (B).

Okay. Then I suggest solving those three equations in a group. It won't hurt to think the problem more deeply or from a different point of view but using NII formula without further information would have been incorrect I think.

 

[Orodruin]

You could solve it by that method by simply assuming a spring constant k. The resulting mass will simply be proportional to it, which will cancel out in the end. However, just using the kinematics of the problem provides a far more elegant solution.

 

[lep11]

You could solve it by that method by simply assuming a spring constant k. The resulting mass will simply be proportional to it, which will cancel out in the end. However, just using the kinematics of the problem provides a far more elegant solution.

But you don't have to assume the value k since it is given...

 

[Orodruin]

What I am saying is that you do not have to use it and that the answer is independent of the value provided.

 

[lep11]

What I am saying is that you do not have to use it and that the answer is independent of the value provided.

Yes it cancels out sorry for my laggy brain