Question

1-Consider the following. 36y'' − y = 0, y(−4) = 1,   y'(−4) = −1 Find the...

1-Consider the following.

36y'' − y = 0,

y(−4) = 1,   y'(−4) = −1

Find the solution of the given initial value problem.

y(t) = ?

2- Consider the vibrating system described by the initial value problem. (A computer algebra system is recommended.)

u'' + u = 9 cos ωt,

u(0) = 5, u'(0) = 4

3-A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a damping constant of

0.25 lb · s/ft and is acted on by an external force of 3 cos 2t lb. (Use g = 32 ft/s2 for the acceleration due to gravity. Let u(t),

measured positive downward, denote the displacement in feet of the mass from its equilibrium position at time t seconds.)

(a) Determine the steady-state response of this system.
u(t) =

(b) If the given mass is replaced by a mass m, determine the value of m for which the amplitude of the steady state response is maximum.
m =     slugs

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