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(1.2) [0.4] Express the function sin(wt + π/6) as a phase-shifted cosine. (1.3) [O.11] An SHO trajectory is given by )sin (), where t is in seconds and r is in metres. Determine the (a) equilibrium position, (b) amplitude, (c) angular frequency, (d) cycle frequency, and (e) period. (1.4) [O.14] The trajectory of an oscillating object was carefully measured and is presented on the adjacent graph. The times are in seconds, while the displacement is measured in millimetres From the...
(1 point) The graph shows the displacement from equilibrium of a mass-spring system as a function of time after the vertically hanging system was set in motion at time t0. Assume that the units of time are seconds, and the units of displacement are centimeters. The first t-intercept is (0.75, 0) and the first minimum has coordinates (1.25,-1) (a) What is the period T of the periodic motion? seconds (b) What is the frequency f in Hertz? What is the...
Consider two sinusoidal currents ?2(?) = 10 cos(10??) mA ?3(?) = 10 sin(10??) mA where t is in seconds. (i) Find the total current given by ?(?) = ?2(?) + ?3(?) (ii) Determine the amplitude, frequency (linear & angular), period, phase angle, and time shift of ?(?)
(1 point) The graph shows the displacement from equilibrium of a mass-spring system as a function of time after the vertically hanging system was set in motion at time t= 0. Assume that the units of time are seconds, and the units of displacement are centimeters. The first t-intercept is (0.75, 0) and the first maximum has coordinates (1.25, 4). (a) What is the period T = of the periodic motion? seconds (b) What is the frequency f in Hertz?...
Problem 3: A system has the transfer function: Gfs) -8 +24s+800 35+6 Assuming time for this system is expressed in seconds, if the system is subjected to a periodic input of 4 sin ot, determine a) The frequency o where the amplitude of the output will be at its maximum b) The functional expression for how the output amplitude varies with-the input frequency, c) The functional expression for how the phase of the output with respect to the input varies...
1. (i) In a circuit, the voltage is given by: Vs (t) 12 cos(50t10) V (a) What is the amplitude of the voltage? (b) What is the phase of the voltage? (c) What is the angular frequency (radians/sec.) of the voltage? (d) What is the frequency (in cycles/sec.) of the voltage? (e) Determine vs (t) at time t 2.5ms (ii) Given v1(t)cos(50t 50°) V and v2(t) 12 sin(50t 10°) V, determine the phase angle between the two sinusoids and determine...
only 3 and 7 please H.W. #1 ELEC 210 I. Evaluate y = 5.6 sinα at each of the following angles. a, α = 90°,y". c, α = π / 3 rad, y =4L8 Find the amplitude and frequency of the following wave: y-3.2 sin (437t) , amplitude is b, α = 550, y =- d, α = 2π rad, y 2. 2 2 ,f= loa。 3. Find the angular veloiy f waveform with a period of T=55 s,ω=-rad/s 4....
2. Figure 2 shows a 6-pulse thyristor rectifier feeding a DC static load an operating at steady-state. The ac input power supply is a symmetric set of three-phase voltages forming a direct sequence, having rms line-to-line voltage of Vuns equal to 415 V and angular frequency ω equal to 100π rad/s. The load is sufficiently inductive to smooth out the load current i(t), i.e. i 1, where I is a constant. a. Derive the mathematical expression of the average DC...
Problem 7 If A cos 0,+B sin oft = rsin(0 -0) = R cos(t-8), (a) determiner and in terms of A and B , and (b) the relationship among R,r, 8 and 2 Ans. (a) r = VA’ + Bº, tan 0 4 b)r=R, 0 = 8-5, tan tan 8 +1 = 0 Problem 8 (a) Define the steady state solution of a given SLDE. (b) Consider the motion of a 2-kg mass in a (m,c,k)-system under a cyclic load....
#40 a-f B-A. (B+A ". Beats slation Recall the identity cos A-cos Be2-2A)sin(-2A) a. Show that 0-10,a, . 9 and (ii)o_10,us2toverify the identity. In which case do you see Gaph the functions on both sides of the equation in part (a) with (i) beats? b. 40 Analysis of the forced damped oscillation equation Consider the equation my"+ey'+ky Fo cos wof, which oscillator. Assume all the parameters in the equation are positive. a. Explain why the solutions of the homogeneous equation...