Calculating Displacement on a Spring: Common Mistakes and Troubleshooting Tips

In summary, the conversation involves a problem where a 0.28 kg mass is suspended on a spring. The mass is then pulled down an additional distance of 14 cm and released. The task is to find the displacement from the equilibrium position after 0.4 seconds. Steps are taken to find the spring constant, natural frequency, and amplitude of oscillation. The final answer is -7.69 cm, which is the displacement from the equilibrium position.
  • #1
Sam
14
0
Problem:

a 0.28 kg mass is suspended on a spring which stretches a distance of 5.6 cm. The mass is then pulled down an additional distance of 14 cm and released. What is the displacement from the equilibrium position with the mass attached (in cm) after 0.4 seconds? Take up to be positive and use g = 9.81 m/s^2

Ok, I have done the following and it's not correct:

This is how I tried to solve...

1. Find k, the spring constant F = kx (Hooke's Law).
Since F = mg, then k = mg/x = 4.905000

2. Find the natural frequency, omega = (k/m)^1/2.
Omega = 13.23550 radians/sec = 2.106495 Hz.

Since energy in the system is conserved, the amplitude of the oscillation is just +/-14 cm centered about the resting deflection of -5.6 cm.

At t = 0 the things starts out fully deflected (i.e., at the peak of the sinusoidal curve), so the equation of the motion would be:
x(t) = -0.056 - 0.14*cos(1.323550*t)
x(0.4) = -0.1329355 m

What did I do wrong? Please help.

Thank you!
 
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  • #2
k is 49.05 N/m not 4.905.


You used x= 5.6 cm when, since you used g= 9.801 m/s2,
you should have used 0.056 meters.
 
  • #3
Still isn't coming out

I then came up with -13.29355 m

That is still incorrect.

Sorry... frustrated.
 
  • #4
I figured it out...

-14*cos(13.2355042*.4) = -7.69

Thanks.
 

1. What is displacement?

Displacement is a measurement of the distance and direction an object has moved from its original position. It is calculated by subtracting the initial position from the final position of an object.

2. What is the difference between displacement and distance?

Distance is a measurement of how far an object has traveled, while displacement is a measurement of the change in position of an object. Distance is a scalar quantity, while displacement is a vector quantity that includes both magnitude and direction.

3. How is displacement calculated?

Displacement is calculated by subtracting the initial position from the final position of an object. It can be represented by the equation Δx = xf - xi, where Δx is the displacement, xf is the final position, and xi is the initial position.

4. What is a positive/negative displacement?

A positive displacement means that the object has moved in the positive direction, while a negative displacement means the object has moved in the negative direction. The direction is determined by the reference point or the starting position of the object.

5. How does displacement relate to velocity?

Displacement and velocity are closely related, as velocity is the rate of change of an object's displacement. In other words, velocity is the displacement divided by the time taken to cover that displacement. This can be represented by the equation v = Δx/Δt, where v is the velocity, Δx is the displacement, and Δt is the time.

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