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Consider the RLC circuit with
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Differential Equations and Linear Algebra (4th Edition)
- Solve for the convolution of sin (t) and cos (t).arrow_forwardAn amusement park has two ferris wheels that both load passengers at the bottom, 3 m above the ground. Both wheels require 40 seconds to complete one revolution. The larger ferris wheel has a diameter of 25 m and the smaller ferris wheel has a diameter of 10 m. The height of a passenger on each wheel can be expressed in the form h(t) = a cos[b(tc)] + d, where h(t) is the height above the ground in metres t seconds after the ride begins. 25 m 3m 14 O a and b O a and d TOT Ob and c Oc and d 10 m 3 m A 76 If the ferris wheels have the same period of rotation, then the two parameters that must be the same in the two functions are Groundarrow_forwardA hamster wheel of radius 25 cm has a rung that is travelling at a constant speed. The rung makes one complete revolution in 3 s. The axle of the hamster wheel is 27 cm above the ground. Write the equation that models this situation, beginning when the rung is at the very top of the wheel. = Omt): Oh(t) = 52 cos(6nt) + 2 On(t) 2π Oh(t) = 52 cos (² t) + 2 25 COS(O) + 21 A rung 25 cos Axle 2π (2 t) + 27 wikiHowarrow_forward
- A strong gust of wind strikes a tall building, causing it to sway back and forth in damped harmonic motion. The frequency of the oscillation is 0.5 cycle per second, and the damping constant is c = 0.6. Find an equation of the form y = ke-ctsin(@t) that describes the motion of the building. (Assume that k = 1, and take t = 0 to be the instant when the gust of wind strikes the building. Assume y begins increasing at t = 0.) y =arrow_forwardA mass that weighs 8 lb stretches a spring 6 inches. The system is acted on by an external force of 8 sin(8t) lb. If the mass is pulled down 3 inches and then released, determine the position of the mass at any time t. Assume that the u-axis is directed downwards and ft Express your answer as a linear combination of sin(at) 9 = 32 s2 and cos(at), where u is in feet and t is in seconds. u(t): Determine the first four times at which the velocity of the mass is zero. Exclude t = 0 as trivial, and enter exact answers. First zero: t = Second zero: t = Third zero: t = Fourth zero: t =arrow_forwardThe average voltage, vavg, of a sinusoidal voice waveform fed into the speaker is found to be : T Vavg V cos(wt + 0)dt = - T Where, the voice signal is V cos(wt + 0) with a period T, a peak voltage V, an angular frequency w , and a phase 0. Evaluate vavg.arrow_forward
- Suppose that in the RLC circuit below, a voltage of Vin = 6 sin(5t) is applied at t = 0, when Vc (0) = 2, V¿(0) = –1. | 20 Ω 2 H Vin .02 F Solve for the voltage across the capacitor, V = Vc(t). Use undeter- mined coefficients.arrow_forwardThe power P in a circuit is P = Ri2, where R is the resistance and i is the current. Find dP/dt at t = ; if R = 1000 2 and i varies according to i = sin(47t) (time in seconds).arrow_forwardAn alternating current E(t)=120sin(12t) has been running through a simple circuit for a long time. The circuit has an inductance of L=0.28 henrys, a resistor of R=9 ohms and a capacitor of capcitance C=0.044 farads.What is the amplitude of the current I?arrow_forward
- Give the number of oscillations occurring per second for a spring-mass system that obeys the simple harmonic motion function f(t) = 6 cos (Tt), where tis in seconds.arrow_forwardSuppose the oscillatory motion of an object can be modeled using the equation s(t) = 5.9sin(0.44t) where time is measured in seconds and distance is measured in inches. Find the time (in seconds) required for the object to complete one oscillation. (Provide 4 decimal places.)arrow_forwardt cos 412 dtarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage