Amount of time for a half period to occur

In summary: Sorry I'm braindead been studying all morning I just want this homework done.Yes, as you can see in the sketch, at t=0 the function is at x=A and at t=T/8 it is at x=0.5.
  • #1
Capncanada
53
0

Homework Statement



A mass-spring system has k = 105 N/m and m = 1.75 kg.

If it is undergoing simple harmonic motion, how much time does it take the mass to go from x = A to x = 0?

Homework Equations



T=2pi*sqrt(m/k)

The Attempt at a Solution



Tried plugging in the values for the equation I gave to find T, then cutting it in half to find the amount of time the question asked for, but it's not the correct answer.
 
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  • #2
What exactly is one cycle? If you understand that, you'll see why your answer is wrong. It may help to look at a diagram that shows one period in your textbook.
 
  • #3
When the mass goes into the spring and back?
 
  • #4
Sketch the x(t) function for a full period and see.

ehild
 
  • #5
Capncanada said:
When the mass goes into the spring and back?
Yes. So in one cycle, if it starts at x(0)=A, it ends at x(T)=A, but more important, what does x(t) do in between? As ehild suggested, plot x(t) for one cycle.
 
  • #6
Who's A and can you link it to T ? EDIT: So A's the amplitude...
 
Last edited:
  • #7
Uhh x goes to A? Which equation can I use to solve for that? x=Acos(ωt)?

Sorry I'm braindead been studying all morning I just want this homework done.
 
  • #8
Capncanada said:
Which equation can I use to solve for that? x=Acos(ωt)?

Yes. x = A cos (2pi* t/T). How does it look like? What is x at t=0, t=T/8, T/4, ...

ehild
 
  • #9
So I can plug in x as A so that A cancels out here and then solve for t where T = 1/2?
 
  • #10
Capncanada said:
So I can plug in x as A so that A cancels out here and then solve for t where T = 1/2?

Is T=1/2??


Would you please show me a cosine function? Please!

ehild
 

1. What is a half period?

A half period refers to the amount of time it takes for a wave or oscillation to complete half of one cycle.

2. How is the amount of time for a half period calculated?

The amount of time for a half period can be calculated by dividing the total time for one full cycle by two.

3. Can the amount of time for a half period vary?

Yes, the amount of time for a half period can vary depending on the frequency and amplitude of the wave or oscillation.

4. What factors can affect the amount of time for a half period?

The amount of time for a half period can be affected by the medium through which the wave or oscillation travels, the amplitude of the wave, and the frequency of the wave.

5. Why is the amount of time for a half period important?

The amount of time for a half period is important because it can provide information about the properties of a wave or oscillation, such as its frequency and amplitude. It is also used in calculations for various scientific and engineering applications.

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