Algebra HELP for physics homework

In summary, the conversation discusses the process of showing that the given solution (α(t)) satisfies the given differential equation (d^2 α)/(dt^2 )=-g/l α). This involves taking the second derivative of α(t) and showing that it is equal to the right hand side of the equation. The conversation also mentions the variables involved in the problem (α, α0, g, and l) and clarifies that the goal is to show that the solution satisfies the equation, not solve for anything.
  • #1
danpab
5
0
I need help on this question for my postlab, thanks !
By direct substitution, show that equation (3) is a solution of the differential equation (2)


α(t)=α0 cos(√(g/l) t) (3)
(d^2 α)/(dt^2 )=-g/l α (2)

α = angle alpha in degrees
α0 = amplitude of motion
g = gravity
l = length
 
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  • #2
If you want help you need to post an attempt.
 
  • #3
i have no idea where to start :S
 
  • #4
It looks like the problem wants you to show that the solution given a(t) actually satisfies the differential equation. To show this you can take the function a(t) and put it into the differential equation, do the derivatives, and show that after taking the derivatives one side of the equation equals the other.
 
  • #5
ok ill try that thanks :)
 
  • #6
attempt:
α(t)=α0 cos(√(g/l) t) (3)
0=-g/l *α0 *cos(√(g/l) t) *dt^2
is this right? how do is solve for the right part??
 
  • #7
No, it's hard to tell what you're doing. This isn't a algebra problem it's a matter of evaluating derivatives and showing that these satisfy the equation. You need to take the 2nd derivative of a(t) with respect to t ([itex] \frac{d^2a(t)}{dt^2} [/itex]) and show that this is equal to the right hand side ([itex] \frac{-g}{l}a(t) [/itex]). You're not solving for anything, rather just showing that this a(t) satisfies the differential equation. Remember that a is not a variable it is a function.
 
  • #8
ok, completely understood now, its been a while since I've taken calculus, u just completely jolted my memory, problem solved :) THANKS
 

1. What is the relationship between algebra and physics?

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols to solve equations. In physics, algebra is used to express and solve mathematical relationships between physical quantities, such as distance, time, and velocity.

2. How can algebra be used in physics problem solving?

Algebra can be used in physics to set up equations that represent physical situations, solve for unknown variables, and analyze the relationships between different physical quantities. It allows for a more systematic and organized approach to problem solving in physics.

3. What are some common algebraic formulas used in physics?

Some common algebraic formulas used in physics include the equations for motion (such as distance = velocity x time), Newton's second law (force = mass x acceleration), and Ohm's law (voltage = current x resistance). These formulas allow us to relate different physical quantities and solve for unknown variables.

4. How can I improve my algebra skills for physics homework?

Practice is key to improving your algebra skills for physics homework. Make sure you have a strong foundation in basic algebra concepts, and then work on applying those concepts to physics problems. You can also seek help from a tutor or join a study group to get additional support and practice.

5. How important is it to understand algebra for understanding physics?

Algebra is crucial for understanding physics as it allows us to express and solve mathematical relationships between physical quantities. Without a solid understanding of algebra, it can be difficult to fully comprehend and analyze the concepts and principles of physics.

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