- #1
cromata
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- 0
-If we have string of length L that has fixed ends, then we can easily find frequencies with which this string can oscillate:
We just need to solve wave equation: ∂2y/∂x2=1/c2*∂2∂t2 (c is determined by strings properties (linear density and tension), with Dirichlet boundary conditions (y(0,t)=0, y(L,t)=0) Of course to determine how the string is oscillating we also need to know initial shape/speed of string (but that only tells us amplitude of each harmonic)
-But what happens when some force is acting on the string? Let's say that some force F(t) is acting at some distance xo from one end of the string? How do we find solution to this problem?
Can it be treated like some sort of boundary condition or should that force be added to wave equation or something else?
We just need to solve wave equation: ∂2y/∂x2=1/c2*∂2∂t2 (c is determined by strings properties (linear density and tension), with Dirichlet boundary conditions (y(0,t)=0, y(L,t)=0) Of course to determine how the string is oscillating we also need to know initial shape/speed of string (but that only tells us amplitude of each harmonic)
-But what happens when some force is acting on the string? Let's say that some force F(t) is acting at some distance xo from one end of the string? How do we find solution to this problem?
Can it be treated like some sort of boundary condition or should that force be added to wave equation or something else?