Help with solving a IH equation

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In summary, the conversation is about finding the solution to the equation d2i/dt2 + 6di/dt + 25i = -292sin4t. The individual has provided a solution that consists of two parts - the solution to the homogeneous equation and the particular solution to the nonhomogeneous equation. The expert confirms that the solution is reasonable and suggests checking that the particular solution works by calculating its derivatives and plugging them into the equation.
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imperiale
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Homework Statement



d2i/dt2 + 6di/dt + 25i = -292sin4t

Homework Equations


The Attempt at a Solution



i got a solution of
Ae^(-3t)cos4t + Be^(-3t)sin4t + 292/9(cos4t) + 146/9(sin4t)
want to know if I am right
 
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  • #2
Your solution looks reasonable. Your solution can be divided into two parts: the solution to the homogeneous equation i'' + 6i' + 25i = 0, and the particular solution to the nonhomogeneous equation you have.

So your general solution is i(t) = ih(t) + ip(t), where ih(t) consists of the first two terms of your solution, and ip(t) consists of the last two terms.

Your homogeneous solution checks with what I got. To confirm that your general solution is correct, all you need to do is check that your particular solution actually works.

From ip(t) = (292/9)cos4t + (146/9)sin4t, calculate ip' and ip''. If ip'' + 6ip' + 25ip equals -292sin4t, your solution is correct.
 

1. What is an IH equation?

An IH (initial height) equation is a mathematical expression that represents the height of an object at the beginning of its motion. It is typically used in physics and engineering to calculate the initial height of an object when given other motion-related variables.

2. How do you solve an IH equation?

To solve an IH equation, you need to first identify all the known variables (such as time, acceleration, and final height) and plug them into the equation. Then, use algebraic operations to isolate the unknown variable (initial height) and solve for it. Make sure to use the correct mathematical formula for the specific type of motion being described.

3. Can you give an example of an IH equation?

One example of an IH equation is: H = H0 + V0t + (1/2)at2, where H is the final height, H0 is the initial height, V0 is the initial velocity, t is the time, and a is the acceleration. This equation is used to calculate the initial height of an object in free fall.

4. What are the units for an IH equation?

The units for an IH equation will vary depending on the specific variables used. In the example given above, the units for H, H0, and V0 would be in meters (m), while the units for t would be in seconds (s) and the units for a would be in meters per second squared (m/s2).

5. How is an IH equation used in real life?

An IH equation is used in many real life scenarios, such as calculating the height of a building or determining the starting height of a projectile. It is also used in engineering to design structures and machines that involve motion, such as roller coasters or airplanes.

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