Heaviside/step function question

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In summary, the conversation is about a trivial question regarding shifting a function. The person is having trouble understanding how to properly shift the function and is looking for help. The solution involves using the hint provided and simplifying the function to end up with upi(t)sin[3(t-pi)], as desired.
  • #1
missavvy
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Homework Statement


Hey so this is a really trivial question.

f(t) = { 0, 0<= t < pi
{ -sin3t, t>=pi

Just having trouble properly shifting this!

The Attempt at a Solution



f(t) = -upi(t)sin(3t)

= -upi(t)sin[3(t-pi+pi)]

= upi(t)sin[3(t-pi+pi)]

How do I take the +pi out?
I know it should end up as:

upi(t)sin[3(t-pi)]

I just don't really understand how from my last step.
thanks for reading!
 
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  • #2
missavvy said:

Homework Statement


Hey so this is a really trivial question.

f(t) = { 0, 0<= t < pi
{ -sin3t, t>=pi

Just having trouble properly shifting this!

The Attempt at a Solution



f(t) = -upi(t)sin(3t)

= -upi(t)sin[3(t-pi+pi)]

= upi(t)sin[3(t-pi+pi)]
What happened to the minus sign?
How do I take the +pi out?
I know it should end up as:

upi(t)sin[3(t-pi)]

I just don't really understand how from my last step.
thanks for reading!
Hint: 3(t-pi+pi)=3(t-pi)+3pi
 

1. What is a Heaviside/step function?

A Heaviside/step function is a mathematical function that has a value of 0 for any input less than 0, and a value of 1 for any input greater than or equal to 0. It is often used to model sudden changes or jumps in a system.

2. How is a Heaviside/step function different from other mathematical functions?

The main difference is that a Heaviside/step function is discontinuous, meaning it has a sudden jump or change in value, while most other functions are continuous. Additionally, it has a value of 0 for negative inputs, which is not the case for many other functions.

3. What are some real-life applications of Heaviside/step functions?

Heaviside/step functions are commonly used in engineering and physics to model processes with sudden changes, such as electrical circuits, mechanical systems, and thermal systems. They are also used in economics to model demand and supply curves, as well as in signal processing to represent digital signals.

4. Can a Heaviside/step function have a value other than 0 or 1?

No, by definition, a Heaviside/step function only has values of 0 or 1. However, it can be multiplied by a constant to adjust the height of the step.

5. Are there any other types of step functions besides the Heaviside/step function?

Yes, there are several other types of step functions, such as the unit step function, the ramp function, and the double ramp function. They have different shapes and properties, but all share the characteristic of having a sudden change or jump in value.

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