Simple Harmonic Motion Problem

In summary, the computer used in a satellite must be able to withstand 32 times the acceleration due to gravity. To test this, the computer is bolted to a frame and vibrated back and forth at a frequency of 11.4 Hz. The minimum amplitude of vibration needed for this test is still unknown and requires the knowledge of the location, velocity, and acceleration as functions of time. The maximum acceleration has units of [meters/second^2] and a important parameter of an oscillation has units of [1/s]. This information can be found in the provided link.
  • #1
kpangrace
17
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A computer to be used in a satellite must be able to withstand accelerations of up to 32 times the acceleration due to gravity. In a test to see if it meets this specification, the computer is bolted to a frame that is vibrated back and forth in simple harmonic motion at a frequency of 11.4 Hz. What is the minimum amplitude of vibration that must be used in this test?



okkkkkk so let's see here, I'm kind of lost and need this last problem solved...

here's what i know

I have the angular frequency, as well as the period, i found those easily enough.

I'm assuming you just multiply 9.8 times 32 and that gives you an acceleration...

but at this point I'm completely stuck...

do I have to use kinetic and potential energy formulas or is it something extremely simple that I'm missing...

any help would be appreciated, and fast!
 
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  • #2
do you know the location as a function of time?
do you know the vwlocity as a function of time?
do you know the acceleration as a function of time?

The MAXIMUM acceleration has units [meters/second^2] ...
What kind of "important parameter" in an oscillation has units [m]?
What kind of "important parameter" of an oscillation has units [1/s]?
 
  • #3
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1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium position due to a restoring force that is directly proportional to the displacement from the equilibrium position. This type of motion can be seen in various systems, such as a mass on a spring or a pendulum.

2. What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A sin(ωt + φ), where x is the displacement from the equilibrium position, A is the amplitude or maximum displacement, ω is the angular frequency, and φ is the phase constant.

3. What is the relationship between period and frequency in simple harmonic motion?

The period of simple harmonic motion, T, is the time it takes for one complete oscillation, while the frequency, f, is the number of oscillations per unit time. The relationship between T and f is T = 1/f. In other words, as the frequency increases, the period decreases, and vice versa.

4. How do we calculate the maximum velocity and acceleration in simple harmonic motion?

The maximum velocity in simple harmonic motion occurs at the equilibrium position, and its value is given by Vmax = ωA. The maximum acceleration occurs at the extreme positions, and its value is given by amax = ω²A.

5. What is the difference between simple harmonic motion and uniform circular motion?

In simple harmonic motion, the restoring force is directly proportional to the displacement from the equilibrium position, while in uniform circular motion, the centripetal force is directed towards the center of the circular path. Additionally, simple harmonic motion occurs in a straight line, while uniform circular motion occurs in a circular path.

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