Mechanical and Electromagnetic Vibrations and Waves

Answers to the Problems

Chapter 1

P1.1. a) x₁ = 2 cos(40πt) + 0.7958 sin (40πt), x₂ = −2 cos(40πt) + 2.387 sin(40πt) and x₃ = 3 cos(40πt) + 3.979 sin(40πt) = 4.98 cos(40πt −0.925); hence, x_max = 4.98 cm and ν_max = 6.26 m/s.

P1.2. a) , where , cos and sin .

P1.3. , where and .

P1.4. a) F = −Kx, where K = 9π²m = 44.4 N/m. b) U_(P) = 0.888 × 10⁻² cos²(3πt) J, U_(C) = 0.00888 sin²(3πt) J, U_(T) = 0.00888 J. c) U_(P) = 22.2 x², U_(C) = 0.00888 − 22.2 x².

P1.5. F = −Kx; hence .

P1.6. a) , where K = K₁ + K₂. b) The lengths of the springs are: a = (K₁/K)L₁ + (K₂/K)(L −L₂), b = (K₂/K)L₂ + (K₁/K)(L −L₁) and ...