What Is the Spring Constant and Acceleration in Horizontal Spring Oscillations?

[fezmaster]

Hey everyone. I have 2 relatively basic questions about horizontal springs. I feel like the questions are actually very simple (it's just high school physics) but I think I'm approaching it the wrong way. Any help would be greatly appreciated.
1. I'm supposed to find the spring constant when a 5.5kg mass is vibrating at the end of a horizontal spring. It reaches a maximum speed of 7.2m/s and has a maximum displacement of 0.23m. Ignore friction.
2. I'm supposed to find the acceleration of a 4.97kg mass when the displacement of the mass is 2.56m. It oscillating on the end of a horizontal spring with a frequency of 0.467s to the left.

1.
I thought I should first find the acceleration, then force (F=ma) and then solve for the spring constant (k=-F/x). To find the acceleration, I used a=V^2/2d. However, that gave me almost 113m/s. Surely that isn't correct... I feel like I should be using equations for energy somewhere, but I'm not sure which ones.
2.
I tried a similar thing here, using a=2d/t^2. I assumed that I should divide time by 2, because that's the time for a complete oscillation, and I'm only calculating half (2.56m and back to equilibrium). However, this gives me an acceleration of almost 94 m/s^2, which also doesn't feel right.

Thanks in advance!

 

[ehild]

Hey everyone. I have 2 relatively basic questions about horizontal springs. I feel like the questions are actually very simple (it's just high school physics) but I think I'm approaching it the wrong way. Any help would be greatly appreciated.
1. I'm supposed to find the spring constant when a 5.5kg mass is vibrating at the end of a horizontal spring. It reaches a maximum speed of 7.2m/s and has a maximum displacement of 0.23m. Ignore friction.
2. I'm supposed to find the acceleration of a 4.97kg mass when the displacement of the mass is 2.56m. It oscillating on the end of a horizontal spring with a frequency of 0.467s to the left.


1.
I thought I should first find the acceleration, then force (F=ma) and then solve for the spring constant (k=-F/x). To find the acceleration, I used a=V^2/2d. However, that gave me almost 113m/s. Surely that isn't correct... I feel like I should be using equations for energy somewhere, but I'm not sure which ones.

a=V²/(2d) is a relation valid for for a motion with constant acceleration. The problem is about a vibrating body, performing simple harmonic motion. The displacement is x= A sin(ωt) where A is the maximum displacement, and ω is 2pi times the frequency. You certainly have learned the formulas also for the velocity and acceleration.

2.
I tried a similar thing here, using a=2d/t^2. I assumed that I should divide time by 2, because that's the time for a complete oscillation, and I'm only calculating half (2.56m and back to equilibrium). However, this gives me an acceleration of almost 94 m/s^2, which also doesn't feel right.

Thanks in advance!

the same problem again: It is simple harmonic motion, use the appropriate formulas.

ehild

 

[fezmaster]

Thanks, although I'm still somewhat confused. Part of that may be because we have not been taught this yet. Unfortunately, we're still expected to do the homework.
I see your equation, but I don't quite understand how it fits into my problems.

I looked up formulas for acceleration and found a=-xω^2. However, when I use that formula for number 2, I get 463m/s^2. That's an even larger number than before.


I tried something different for number 1. I used Et=1/2mvmax^2 and Et=1/2kA^2 to get 1/2mvmax^2=1/2kA^2. I rearranged to solve for k and got 5.4E3N/m. Does that work?

 

[golanor]

Thanks, although I'm still somewhat confused. Part of that may be because we have not been taught this yet. Unfortunately, we're still expected to do the homework.
I see your equation, but I don't quite understand how it fits into my problems.

I looked up formulas for acceleration and found a=-xω^2. However, when I use that formula for number 2, I get 463m/s^2. That's an even larger number than before.


I tried something different for number 1. I used Et=1/2mvmax^2 and Et=1/2kA^2 to get 1/2mvmax^2=1/2kA^2. I rearranged to solve for k and got 5.4E3N/m. Does that work?

Don't just use equations, understand why you are using them.
What you did here is saying that the potential energy of the spring at maximum displacement is equal to the energy of the body at maximum velocity. Why is that true?

Regarding the formulas you are using for #2
Since you need to find the acceleration, think about what laws you can use to find out the acceleration, and then figure out what is missing from the equation you will have for the acceleration in order to solve it, using what you were given.
A small hint - try to think how you can use the frequency of oscillation to find K.

Have fun.

 

[ehild]

Thanks, although I'm still somewhat confused. Part of that may be because we have not been taught this yet. Unfortunately, we're still expected to do the homework.
I see your equation, but I don't quite understand how it fits into my problems.

I looked up formulas for acceleration and found a=-xω^2. However, when I use that formula for number 2, I get 463m/s^2. That's an even larger number than before.

The equation a=-xω² is correct, it comes from the formula for the spring force : F=-kx =ma, and from the equation for the angular frequency, ω²=k/m. x=2.56 m, the frequency is f=0.467 1/s, the angular frequency is ω=2∏f. Just plug-in.

I tried something different for number 1. I used Et=1/2mvmax^2 and Et=1/2kA^2 to get 1/2mvmax^2=1/2kA^2. I rearranged to solve for k and got 5.4E3N/m. Does that work?

That is OK.