- #1
mango84
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Dirac Delta Function:
If, at time t =a, the upper end of an undamped spring-mass system is jerked upward suddenly and returned to its original position, the equation that models the situation is mx'' + kx = kH delta(t-a); x(0) = x(sub zero), x'(0) = x(sub 1), where m is the mass, k is the spring constant, and H is a constant.
(a) Solve the IVP manually, with x(0)=0=x'(0)
(b) Use the solution found in part (a) to explain the significance of the constant H.
(c) Choose a value for H such that the mass achieves a prescribed displacement from equilibrium A for t (greater than or equal to) a.
Does anybody know how to do this? I'm lost!
If, at time t =a, the upper end of an undamped spring-mass system is jerked upward suddenly and returned to its original position, the equation that models the situation is mx'' + kx = kH delta(t-a); x(0) = x(sub zero), x'(0) = x(sub 1), where m is the mass, k is the spring constant, and H is a constant.
(a) Solve the IVP manually, with x(0)=0=x'(0)
(b) Use the solution found in part (a) to explain the significance of the constant H.
(c) Choose a value for H such that the mass achieves a prescribed displacement from equilibrium A for t (greater than or equal to) a.
Does anybody know how to do this? I'm lost!