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# Consider the ODE:y" + 4y cos(wt)Where w is a positive real number. If w is a positive rational number (ie W is & number of the form for positive integers a...

## Question

###### Consider the ODE:y" + 4y cos(wt)Where w is a positive real number. If w is a positive rational number (ie W is & number of the form for positive integers and n), and not equal to 2, show that any solution of the above ODE is periodic Hint: You 'Il find that the solution is the sum of two periodic functions with different periods; try multiple of those periods If w 2, find the general solution and show that it is unbounded as t 3 O0. In other words, if $(t) is any solution, show tha Consider the ODE: y" + 4y cos(wt) Where w is a positive real number. If w is a positive rational number (ie W is & number of the form for positive integers and n), and not equal to 2, show that any solution of the above ODE is periodic Hint: You 'Il find that the solution is the sum of two periodic functions with different periods; try multiple of those periods If w 2, find the general solution and show that it is unbounded as t 3 O0. In other words, if$(t) is any solution, show that given any M > 0 and N > 0, YoU can find a t 2 N with |d(t)l 2 M_  #### Similar Solved Questions

##### Point) Let Vf = 1re sin (Sy) { 25e 5y) j- Find the change between (0, 0) and (1,7/2) Do ways(a) First, find the change by computing the line integral Jc Vf . dr , vhere C i5 curve connecting (0,0) and (1,7/2). The slmplest curve the line segment joining Inese points . Parametenze t: with 0 < <1,70)So Inat Jc Vf . d7 =Note that Inis Isn t a very pleasant integral t0 evaluate by hand (inougn we could eastly tind = numerical estimate for it} It's easier to find Jc Ff dF as the Jc Vf d7 +
point) Let Vf = 1re sin (Sy) { 25e 5y) j- Find the change between (0, 0) and (1,7/2) Do ways (a) First, find the change by computing the line integral Jc Vf . dr , vhere C i5 curve connecting (0,0) and (1,7/2). The slmplest curve the line segment joining Inese points . Parametenze t: with 0 < <...
##### UdThis Question: 7 ptsEvaluate the integral 2 ~sin ~/ - -7Jdat Jzan(2-7) O-wp
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##### 3 Let r() = !sin ti + fcos tj + rk Find r (7) .
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##### 5)(x + 8) X= -1,6. 1)(x -6)Answer the questions below about the function whose derivative is f (x)What are the critical points of f? On what open intervals is f increasing or decreasing? At what points if any, does assume ocal maximum and minimum values?
5)(x + 8) X= -1,6. 1)(x -6) Answer the questions below about the function whose derivative is f (x) What are the critical points of f? On what open intervals is f increasing or decreasing? At what points if any, does assume ocal maximum and minimum values?...
##### Calculate the pressure exerted by 1.0 mol.10 H2S behaving as a perfect gas, at 273.15 K in 22.414 dm3. R=.0821 atm.Llmol.K] (abii 1.5)dubl JsjjCalculate the expansion work done when.11 50 g of iron reacts with hydrochloric acid in an open beaker at 25'C (abii 1.5) at. wt = 55.85 g/mol, R= 8.314 J/mol.KdwbI Jsjj
Calculate the pressure exerted by 1.0 mol.10 H2S behaving as a perfect gas, at 273.15 K in 22.414 dm3. R=.0821 atm.Llmol.K] (abii 1.5) dubl Jsjj Calculate the expansion work done when.11 50 g of iron reacts with hydrochloric acid in an open beaker at 25'C (abii 1.5) at. wt = 55.85 g/mol, R= 8.3...
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##### Given an electromagnetic wave propagating in free space, if H = Hm ei(t +Bz) jFind EE = (BHm/wgo) eit +8z) kE = - (BHm/w) ei(t - +Bz) jE = - (BHm/Weo) ei(wt +8z)E = (BHm/Weo) ei(t +Bz) j
Given an electromagnetic wave propagating in free space, if H = Hm ei(t +Bz) j Find E E = (BHm/wgo) eit +8z) k E = - (BHm/w) ei(t - +Bz) j E = - (BHm/Weo) ei(wt +8z) E = (BHm/Weo) ei(t +Bz) j...
##### Review Formulas (6) and (7) in Section 2.1 and use the Mean-Value Theorem to show that if $f$ is differentiable on $(-\infty,+\infty),$ then for any interval $\left[x_{0}, x_{1}\right]$ there is at least one point in $\left(x_{0}, x_{1}\right)$ where the instantaneous rate of change of $y$ with respect to $x$ is equal to the average rate of change over the interval.
Review Formulas (6) and (7) in Section 2.1 and use the Mean-Value Theorem to show that if $f$ is differentiable on $(-\infty,+\infty),$ then for any interval $\left[x_{0}, x_{1}\right]$ there is at least one point in $\left(x_{0}, x_{1}\right)$ where the instantaneous rate of change of $y$ with resp...
##### In a test tube were combined ~1 mL of diethyl ether; mL of distilled water, and few drops of 0.006 M methylene blue_ The test tube was capped and mixed vigorously for 10 seconds. The layers were allowed to settle; and picture of the test tube was taken_ In your ab report; determine if the dye is in the aqueous_ organic or both layersFigure Picture 0f the test tube containing diethyl ether; distilled water; and methylene blue
In a test tube were combined ~1 mL of diethyl ether; mL of distilled water, and few drops of 0.006 M methylene blue_ The test tube was capped and mixed vigorously for 10 seconds. The layers were allowed to settle; and picture of the test tube was taken_ In your ab report; determine if the dye is in ...
##### (a) Explain how single-walled carbon nanotubes are classified in zigzag and armchair tubes.(b) What inherent properties of single-walled carbon nanotubes make those formed by arc discharge or laser vaporization methods unsuitable for immediate applications?(c) Give examples of how the problems noted in(b) can be overcome.
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##### (#6) Polar coordinates & curves_[3 pts:] If (2,y) = (~4v3, -4) then find the corresponding values ofr > 0 and 0 < 0 < 2t in radians
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4 0 i2 71 74 '4 + 1 { every 3 4 2 1 M 03 3 } #, 11 3 1 8 Ron 74 "~pna { 0 D...
##### Outside temperature over a day can be modeled as asinusoidal function. Suppose you know the temperature is 56 degreesat midnight and the high and low temperature during the day are 64and 48 degrees, respectively. Assuming t is the number of hourssince midnight, find an equation for the temperature, D, in termsof t.
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 56 degrees at midnight and the high and low temperature during the day are 64 and 48 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperatu...