Spring Mass System - Definition, Spring Mass System in Parallel and Series Combination
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SOLVED:The undamped mass-spring system in Fig. 10 is subject to an external force F sin(αt) . The equation of motion is m ẍ k x=F sin(αt) (α≠√((k)/(m))) where x is the displacement of mass m from its equilibrium level and k is the spring stiffness. By assuming the trial function X=C sin(αt) and the initial conditions, when t=0, both x=0 and ẋ=0, show that x=(F)/(ω(k-m α^2))[ωsin(αt)-αsin(ωt)] where ω=√((k)/(m))
SOLVED:The undamped mass-spring system in Fig. 10 is subjec…
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As we know from Section 20, the forced vibrations of an undamped spring-mass system are described by the differential equation M x^'' k x=f(t), where x(t) is the displacement and f(t) is the impressed external force or "forcing function." If x(0)=x^'(0)=0, find the functions A(t) and h(t) and write down the solution x(t) for any f(t). | Numerade
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