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7. Consider the equation x"+w²x = cos Bt. a) Find the solution when the initial conditions are r(0) = r'(0) = 0 when w‡ B. b) Use the trigonometric identity 2 sin A sin B = cos(A-B) - cos(A+B) to write the solution as a product of sines. (b) on

7. Consider the equation x"+w²x = cos Bt. a) Find the solution when the initial conditions are r(0) = r'(0) = 0 when w‡ B. b) Use the trigonometric identity 2 sin A sin B = cos(A-B) - cos(A+B) to write the solution as a product of sines. (b) on

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 49E
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Please do 7 a and b
0 0.5 1 1.5 Figure 2.9 Plot of the solution r(t): (c) showing the phenomenon of beats. 2 1 2.5 3 3.5 Find the solution and plot the result. 7. Consider the equation 4 10-3(cos(45t) - cos(55t)) to Exercise 4. Consider a general LC circuit with input voltage Vo sin Bt. If B and the capacitance C are known, what value of the inductance L causes pure resonance? = 5. An undamped spring-mass system with m = 4 and and stiffness k is forced by a sinusoidal function 412 sin 5t. What value of k causes pure resonance? 6. Consider a spring-mass system with small damping and driven by a cosine force: z" +0.01x' + 4x = cos 2t, x(0) = 0, x'(0) = 0. x"+w²x = cos Bt. a) Find the solution when the initial conditions are x(0) = x'(0) = 0 when w‡ B. b) Use the trigonometric identity 2 sin A sin B = cos(A-B) - cos(A+B) to write the solution as a product of sines. c) Take w= 55 and B 45 and plot the solution from part (b) on the time interval [0, 4]. The solution can be interpreted as a high fre quency response contained in a low frequency amplitude envelope. We
Transcribed Image Text:0 0.5 1 1.5 Figure 2.9 Plot of the solution r(t): (c) showing the phenomenon of beats. 2 1 2.5 3 3.5 Find the solution and plot the result. 7. Consider the equation 4 10-3(cos(45t) - cos(55t)) to Exercise 4. Consider a general LC circuit with input voltage Vo sin Bt. If B and the capacitance C are known, what value of the inductance L causes pure resonance? = 5. An undamped spring-mass system with m = 4 and and stiffness k is forced by a sinusoidal function 412 sin 5t. What value of k causes pure resonance? 6. Consider a spring-mass system with small damping and driven by a cosine force: z" +0.01x' + 4x = cos 2t, x(0) = 0, x'(0) = 0. x"+w²x = cos Bt. a) Find the solution when the initial conditions are x(0) = x'(0) = 0 when w‡ B. b) Use the trigonometric identity 2 sin A sin B = cos(A-B) - cos(A+B) to write the solution as a product of sines. c) Take w= 55 and B 45 and plot the solution from part (b) on the time interval [0, 4]. The solution can be interpreted as a high fre quency response contained in a low frequency amplitude envelope. We
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