Motion of an object attached to a spring

In summary, a 5.0 kg mass suspended by a spring that stretches 10 cm when the mass is attached is displaced an additional 5.0 cm and released. Its position as a function of time can be approximated by X(t) = 0.05cos10t, where w (angular frequency) is equal to the square root of k/m. The force in this situation comes from the weight of the body, and x represents the extension of the spring. Hooke's Law is used to find k, and then the other formula is used to solve for w.
  • #1
myoplex11
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Homework Statement


A body of mass 5.0 kg is suspended by a spring which stretches 10 cm when the mass is attached. It is then displaced downward an additional 5.0 cm and released. Its position as a function of time is approximately?


Homework Equations


X(t) = Acos(wt+φ)


3. The Attempt at a Solution
the awnser to this problem is 0.05cos10t. I see where they get the 0.05 from since it is the amplitude but how do they figure out w(angular frequency)=10
 
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  • #2
w = sqrt (k/m)

F = -kx

Now you have the equations you need
 
  • #3
how do i figure out F acceleration is not given
 
  • #4
F = -kx

is Hooke's Law.

The force comes from the weight of the body. And x is the extension of a spring.


Use this to find k.

Then apply the other formula to find w.
 

1. What is the relationship between the motion of an object attached to a spring and the spring constant?

The motion of an object attached to a spring is directly proportional to the spring constant. This means that as the spring constant increases, the amplitude (maximum displacement) of the object also increases, and vice versa.

2. How does the mass of the object affect its motion when attached to a spring?

The mass of the object affects its motion by changing the period of the oscillations. A heavier object will have a longer period, meaning it will take longer to complete one full cycle of oscillation compared to a lighter object.

3. What is the difference between simple harmonic motion and damped harmonic motion?

Simple harmonic motion is when an object attached to a spring oscillates back and forth without any external forces acting on it. Damped harmonic motion, on the other hand, is when external forces (such as friction) cause the amplitude of the oscillations to decrease over time.

4. How does the initial displacement of the object affect its motion when attached to a spring?

The initial displacement, or starting position, of the object attached to a spring will determine the amplitude and phase of the oscillations. A larger initial displacement will result in a larger amplitude, while a smaller initial displacement will result in a smaller amplitude.

5. Can the motion of an object attached to a spring ever reach a constant velocity?

No, the motion of an object attached to a spring will never reach a constant velocity. This is because the spring will always exert a restoring force on the object, causing it to continue oscillating back and forth rather than reaching a constant velocity.

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