Displacement of mass spring system

[Schmidt]

The displacement y(t) of a driven mass-spring system is described by the differential
equation

2y'' + 14y = 8 cos(2t)

with initial value conditions y(0) = 0; y'(0) = 0.

(a) Is this system damped or undamped?
(b) Is this system resonant?
(c) Write the solution to the IVP in terms of a product of two sine functions
(d) What is the frequency of the beats?Could someone please guide me with this question? I'm fine with part a (since the coefficient of y' = 0) but am rather confused about the other subsections. I also couldn't find anything of use in the prescribed textbook.

ThanksEdit: I found a source that said natural frequency = (k/m)^1/2 , and this is not equal to the frequency of the driving force (2) and therefore it is not resonant. I also found the formula to express this as a product of two sines.

Now d is only part I am stuck on.

 

[Opalg]

The displacement y(t) of a driven mass-spring system is described by the differential
equation

2y'' + 14y = 8 cos(2t)

with initial value conditions y(0) = 0; y'(0) = 0.

(a) Is this system damped or undamped?
(b) Is this system resonant?
(c) Write the solution to the IVP in terms of a product of two sine functions
(d) What is the frequency of the beats?Could someone please guide me with this question? I'm fine with part a (since the coefficient of y' = 0) but am rather confused about the other subsections. I also couldn't find anything of use in the prescribed textbook.

ThanksEdit: I found a source that said natural frequency = (k/m)^1/2 , and this is not equal to the frequency of the driving force (2) and therefore it is not resonant. I also found the formula to express this as a product of two sines.

Now d is only part I am stuck on.

Hi Schmidt, and welcome to MHB! According to Beat (acoustics) - Wikipedia, the free encyclopedia, the beat frequency is just the difference between the natural frequency and the driving force frequency.