At time t the displacement from equilibrium, y(t), of an undamped spring-mass system of mass m is governed by the initial-value problem den nye+w+y = fo coswt, y0) = 1, diy (0) = 0 та where fo and w are positive constants. solve this initial value problem to determine the motion of the system. what happens as t o

a)

b) As t →∞ y(t) becomes undefined as value of cos is undefined at ∞

Step-by-step explanation:

Considering the complete question attached in fig below:

Non-homogeneous differential equation for given undamped system is:

  ---(1)

To find general solution, consider the homogeneous part:

General solution is

Using method of undetermined co-efficient,find the particular solution:

Substituting all these values in (1)

Equating the terms on both sides

solution of given differential eq. :

Using initial values :

then (2) becomes

As t →∞

y(t) becomes undefined as value of cos is undefined at ∞