alc_sol_man_ch04

# alc_sol_man_ch04 - Solutions Manual 4.1(a(b(c(d(e(f(g 4.2...

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Solutions Manual Introduction to Mechatronics and Measurement Systems 19 4.1 (a) linear (b) nonlinear (c) linear (d) linear (e) nonlinear (f) nonlinear (g) linear 4.2 The Fourier Series is: and the fundamental frequency is 4.3 Since V rms = 120V and f = 60Hz, the Fourier Series is: and the fundamental frequency is 60Hz. 4.4 So But , so But sine of any multiple of π is 0, so A n = 0 ±² () ³´ π ² µ¶· ¸ ¹ º ω º ´ π ------ »¼½ ¸¸ ´¾ ¿Àµ ´ π ¹² µ¶· »ÁÂÃÄ »´º π ² µ¶· Å · ´ Æ --- · ω º ² ÇÈµ ² É º Æ ´ Æ · ω º ² ÇÈµ ² É º Æ ´ -- · ω º ² ÇÈµ ² É Æ ´ Æ Ê Å · ´ · ω º Æ ------------- · ω º ² µ¶· [] º Æ ´ · ω º ² µ¶· Æ ´ Æ Ê    ¸ ω º ´ π Æ ¸ Å · » · π · π µ¶· ´· π µ¶· Ê· π µ¶· Ë ¸

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Solutions Manual 20 Introduction to Mechatronics and Meaurement Systems 4.5 Using MathCAD: 4.6 (a) So the bandwidth is: 0 Hz to 7.17 Hz t 0 0.01 , 3.0 .. Va t () 1 π sin 2 π . t . 2 n2 4 , 10 .. Vb t 1 π sin 2 π . t . 2 2 π n cos 2 n . π . t . n1 n 1 . . m2 4 , 50 .. Vc t 1 π sin 2 π . t . 2 2 π m cos 2 m . π . t . m1 m 1 . . 0123 0.5 0 0.5 1 Va t t 0.5 0 0.5 1 1.5 Vb t t 0.5 0 0.5 1 1.5 Vc t t ± ² ³ ´ ´ µ ------   ´ --------------------- ´· ³ ¸¹ º ´ ¹ ² » ¼¼
Solutions Manual Introduction to Mechatronics and Measurement Systems 21 (b) T = 1s , (c) Using MathCAD: 4.7 (a) n ω (rad/sec) f (Hz) A in A out /A in A out = (A out /A in )A in 1 ω 0 1 4/ π 1 4/ π 2 0 3 4/3 π 1 4/3 π 3 0 5 4/5 π 1 4/5 π 4 0 7 4/7 π 3/4 3/7 π 5 0 9 4/9 π 1/4 1/9 π >5 (2n-1) ω 0 (2n-1) 4/f π 00 ± ² ³ ´ --- ³µ¶ ·· ω ¸ ¹ π ± ¸ ¹ π º»¼ ½¾¿ ------- À ²ÁÂ Ã π -- ¹ π Â () ½ÄÅ Ã Æ π ------ Ç π Â ½ÄÅ Ã È π ³¸ π Â ½ÄÅ Æ É π ³Ã π Â ½ÄÅ ³ Ê π ³Ë π Â ½ÄÅ Ì ÌÌÌ · t 0 0.01 , 2 .. Vout t 4 π sin 2 π . t . . 4 3 π . sin 6 π . t . . 4 5 π . sin 10 π . t . . 3 7 π . sin 14 π . t . . 1 9 π . sin 18 π . t . . 012 2 0 2 Vout t 2.0 t ω ¿ ³ ÍÎ ³¸¸¸ ½¾¿

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Solutions Manual 22 Introduction to Mechatronics and Meaurement Systems (b) T = 1s, f = 1Hz, ω 0 = 2 π where (c) Using MathCAD: 4.8 ±² () ³ ´µ µ ³ ¶·² ³ ---------- µ   ω µ ² ¸´µ µ¹ º º ³ µ » ¼µ ¹ ½ π ----------------------- º ³ ³ µ ¹ ¹ ω µ ω ¾ ------ ¼ ¿ --------------------------- º ω µ ½ ¼ π º n 1 100 .. ω c 1000 ω n 2n . 1 2 . π . t 0 0.01 , 2 .. Ft n 4 . 1 π . 1 1 ω n ω c 2 . sin ω n t . . 012 1 0 1 t ω À ¹ ¼ ÁÂÃ ¸Ä¾ ------- ÅÆÇÅÇ ¸Ä¾ ÅÆ¹¹ÈÉÊ ºº º ω É È¹ Æ Ë ¹ ¹ ¼ ½ ¿ ¸Ä¾ ÈÆ»» ¸Ä¾ ÅÆË»ÇÉÊ º ω À ÌÂµÃÍ´Ã²Î ω É ≤≤
Solutions Manual Introduction to Mechatronics and Measurement Systems 23 4.9 (a) (b) and (c) 4.10

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alc_sol_man_ch04 - Solutions Manual 4.1(a(b(c(d(e(f(g 4.2...

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