Finding Initial Block Position and Maximum Speed of Oscillation

In summary: The value you obtained for the maximum speed should be in meters per second, as the units for spring constant are newtons per meter.In summary, the conversation discussed a problem involving a block attached to an ideal spring on a smooth horizontal table. The block was released from a compressed position and reached a certain position and speed. The problem asked for the initial position and maximum speed of oscillation. Using the equations for energy and the properties of a spring, the initial position was found to be -0.0822m and the maximum speed was correctly determined by setting the displacement to 0. The incorrect result for the initial position may have been due to a mistake in units.
  • #1
NY152
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1. The problem statement, all variables and given/known
On a very smooth horizontal table, a block of mass m=0.75 kg is attached to an ideal spring with a spring constant k= 242 N/m. The origin of the horizontal coordinate (x=0) is set at the equilibrium position of the block. The block is initially held at a negative position where it keeps the spring compressed. Then the block is released, and moves through position x1=0.105m with a speed v1=1.42 m/s.

a) What was the initial position of the block, x0?

b)What is the maximum speed of oscillation, vmax?


Homework Equations


omega = sqrt(k/m
F=-kx
Vmax=A*omega
x=Acos(2pi*f*t)

The Attempt at a Solution


I thought about using conservation of energy by doing KE+PE=W
W=Fs and KE=1/2mv^2 but I don't think this would give me displacement in terms of a negative/before equilibrium position
 
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  • #2
Hi NY152,

Welcome to Physics Forums.

NY152 said:
I thought about using conservation of energy by doing KE+PE=W
W=Fs and KE=1/2mv^2 but I don't think this would give me displacement in terms of a negative/before equilibrium position

If you take a close look at the formulas for the components of the energy, both involve the squaring of a term. A negative value squared yields the same amount as a positive value of the same magnitude.
 
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  • #3
gneill said:
Hi NY152,

Welcome to Physics Forums.
If you take a close look at the formulas for the components of the energy, both involve the squaring of a term. A negative value squared yields the same amount as a positive value of the same magnitude.
Thanks for the input! Do you think I'm on the right track then in terms of those formulas or am I missing something??
 
  • #4
You're on the right track. You're just missing stating the formula for the PE of a spring.
 
  • #5
gneill said:
You're on the right track. You're just missing stating the formula for the PE of a spring.
I only have one attempt left, so I'm just going to post my work here in the hopes that someone might see if I'm doing it right or wrong.

So I did: KE+PE=W W=Fs
1/2mv^2+1/2kx^2=(-kx)(s)
and found s to be =-0.0822
 
  • #6
NY152 said:
I only have one attempt left, so I'm just going to post my work here in the hopes that someone might see if I'm doing it right or wrong.

So I did: KE+PE=W W=Fs
1/2mv^2+1/2kx^2=(-kx)(s)
and found s to be =-0.0822
No, the sum of the KE and PE is a constant, the total energy of the system. Better to write:

E = KE + PE

In an isolated system the KE and PE can trade energy back and forth, but their sum is always a constant.

You are given a particular data point with both displacement and velocity. So you can find the value of E which will hold for every point throughout the cycles.
 
  • #7
gneill said:
No, the sum of the KE and PE is a constant, the total energy of the system. Better to write:

E = KE + PE

In an isolated system the KE and PE can trade energy back and forth, but their sum is always a constant.

You are given a particular data point with both displacement and velocity. So you can find the value of E which will hold for every point throughout the cycles.
gneill said:
No, the sum of the KE and PE is a constant, the total energy of the system. Better to write:

E = KE + PE

In an isolated system the KE and PE can trade energy back and forth, but their sum is always a constant.

You are given a particular data point with both displacement and velocity. So you can find the value of E which will hold for every point throughout the cycles.
Sorry for the late reply, so I solved for E and got 2.09, now do I just set that equal to PE + KE when the spring is retracted? In which case would velocity be zero? If so I get x=-0.131
 
  • #8
NY152 said:
Sorry for the late reply, so I solved for E and got 2.09, now do I just set that equal to PE + KE when the spring is retracted? In which case would velocity be zero? If so I get x=-0.131
Yup. Good.
 
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  • #9
NY152 said:
Sorry for the late reply, so I solved for E and got 2.09, now do I just set that equal to PE + KE when the spring is retracted? In which case would velocity be zero? If so I get x=-0.131
Alright well it wasn't -0.131, but I got the max velocity right by setting x=0 so I'm not sure where I went wrong but thanks for the help!
 
  • #10
NY152 said:
Alright well it wasn't -0.131, but I got the max velocity right by setting x=0 so I'm not sure where I went wrong but thanks for the help!

Your initial position should be correct. Did you remember to include the units?
 

1. What is oscillation displacement?

Oscillation displacement refers to the distance an object moves from its original position during an oscillation, which is a repetitive back-and-forth motion around a central equilibrium point. It is a measure of the amplitude, or strength, of the oscillation.

2. How is oscillation displacement measured?

Oscillation displacement can be measured using various methods, depending on the type of oscillation. For example, in simple harmonic motion, the displacement can be measured using a ruler or measuring tape. In more complex oscillations, such as those in a pendulum or a spring, displacement can be measured using sensors and data collection software.

3. What factors affect the oscillation displacement?

The oscillation displacement is influenced by several factors, including the amplitude of the oscillation, the frequency of the oscillation, and the damping force. The mass and stiffness of the oscillating object can also affect the displacement. In addition, external forces such as friction or air resistance can also impact the displacement.

4. How is oscillation displacement related to energy?

Oscillation displacement and energy are closely related. As the displacement increases, the potential energy of the object also increases. As the object moves back towards its equilibrium point, this potential energy is converted into kinetic energy. The maximum displacement of the oscillation is also known as the turning point, where the kinetic energy is at its maximum and the potential energy is at its minimum.

5. What are some real-life examples of oscillation displacement?

Oscillation displacement can be observed in various systems and objects in everyday life. Some examples include a swing set, a metronome, a grandfather clock pendulum, and a tuning fork. In the field of engineering, oscillation displacement is also important in designing structures to withstand vibrations and oscillations caused by earthquakes or wind. In addition, many electronic devices, such as speakers and microphones, use oscillation displacement to produce and detect sound waves.

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