Spring Help-Please: Period, Frequency, Amplitude, Acceleration & Energy

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In summary, the motion of a 650-g mass on a horizontal spring struck by a hammer with an initial speed of 2.26 m/s has a period of 0.37 seconds and a frequency of 2.70 Hz. The amplitude is 0.13 m and the maximum acceleration is 36.8 m/s^2. The position as a function of time is given by x=0.13cos(phi) and the total energy is constant at 0.25J. The kinetic energy when x=0.4A is 0.25J.
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bard
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At t=0, a 650-g(0.65kg) mass at rest on the end of a horizontal spring(k=184n/m) is struck by a hammer which gives it an initial speed of 2.26 m/s. Determine (a) the period and frequency of the motion (b)the amplitude (c)the maximum acceleration (d) the position as a function of time (e) the total energy, and (f)the kinetic energy when x=0.4A where A is the amplitude.

a) period=2pi*sqrt0.65/184=.37
Frequency=2.07
b)v=sqrtk/m(A^2-X^2)=0.13

C) A-max=184*0.13/0.65=36.8 m/s^2

d)x=0.13cos(phi)

e)no idea

f)no idea
 
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  • #2
Revisit the formula for Total energy and K.E.

Total Energy remains Constant
 
  • #3
so the total energy would be

1/2 KA^2
 
  • #4
yes and what about the K.E.
 
  • #5
Two other points:

I get that the frequency is 2.70 not 2.07. A typo?

The position, measured from the rest point, is .13 sin(16.8t).

There was no "phi" in the problem. What was that?
 
  • #6
So the kinetic energy would be

1/2*184(0.052)^2=.25J
 

What is the period of a spring?

The period of a spring is the time it takes for one complete oscillation, or back and forth motion, to occur. It is typically measured in seconds.

How is frequency related to a spring?

Frequency is the number of oscillations that occur per unit of time, typically measured in hertz (Hz). In the case of a spring, the frequency is inversely proportional to the period, meaning that as the frequency increases, the period decreases.

What is the amplitude of a spring?

The amplitude of a spring is the maximum displacement from its equilibrium position during one oscillation. It is typically measured in meters and can be affected by factors such as the mass and stiffness of the spring.

How does acceleration play a role in a spring's motion?

The acceleration of a spring is directly proportional to the force applied to it. This means that as the spring is stretched or compressed, the acceleration increases or decreases accordingly.

What is the role of energy in a spring's motion?

Energy is essential in a spring's motion as it is what allows the spring to oscillate back and forth. The potential energy stored in the spring is converted into kinetic energy as it compresses and expands, allowing for continuous motion until the energy is eventually dissipated through friction and other forces.

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