Exercise 3: Damped forced vibration. Find the solution of u′′ +(1/8)u′ + u = 3 cos(ωt), u(0) = 2, u′(0) = 0 using sympy.dsolve for ω = 0.3 and ω = 1. Plot the solution, transient solution and steady-state solution in a common plot for 0 < t < 10 for ω = 0.3 and ω = 1 respectively.
Exercise 3: Damped forced vibration. Find the solution of
u′′ +(1/8)u′ + u = 3 cos(ωt), u(0) = 2, u′(0) = 0
using sympy.dsolve for ω = 0.3 and ω = 1. Plot the solution, transient solution and steady-state
solution in a common plot for 0 < t < 10 for ω = 0.3 and ω = 1 respectively.
Exercise 4: Undamped forced vibration. Plot the solution ofu
′′ + u = 3 cos(ωt), u(0) = 0, u′(0) = 0 for 0 < t < 10 for ω = 0.3 and ω = 1 respectively.
(You may find the solution either numerically with scipy.integrate.solve ivp, scipy.integrate.odeint or by finding and plotting the symbolic solution via sympy.dsolve)
Remark: The vibration consists of beats; in the critical case ω = 1 solutions do not stay bounded
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