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3 cards from this section. Quick, good the night before a test.
What is the finite difference method?
Think about how we might break up time into smaller sections.
Why might we need to discretize time?
Consider why continuous equations can be challenging.
What does the finite difference method primarily address?
Recall the primary uses of the method.
True or False: The finite difference method can model continuous systems with variable properties more effectively than analytical methods.
Think about the advantages over analytical methods.
Using the finite difference method, if a system has a natural frequency of 5 rad/s and initial displacements of x(0)=0 and x(1)=0.1, calculate the displacement at the next time step given a Δt of 0.1 seconds.
Start by identifying your constants and then plug into the formula appropriately.
Discuss the impact of increasing the time step size on the accuracy of results obtained from the finite difference method.
Consider how a larger time step could skip details of the system's motion.
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