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Problem 2. Consider the function plotted below A) What is the amplitude of this function? B)...
Problem 2. Consider the function plotted below. A) What is the amplitude of this function? B)...
Problem 2. Consider the function plotted below. A) What is the amplitude of this function? B) What is (approximately) the wavelength of this function? C) What is (approximately) the spatial frequency of this function? D) Express (approximately) this function in sine form. E) Express (approximately) this function in cosine form. 0. -2 -5 -2.5 0. 2.5 a (m)
(1.2) [0.4] Express the function sin(wt + π/6) as a phase-shifted cosine. (1.3) [O.11] An SHO...
(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...
Problem 4 -π/3) in quadrature form. 2π A) Express the function Y1 = (2 m) sin(...
Problem 4 -π/3) in quadrature form. 2π A) Express the function Y1 = (2 m) sin( 5-x B) Express the function y3=(4m)cos(10-)-(2m) sin( nx) incosine form. 10 in sine form. C) Express the function y3= (4 m) cos(nz)-(2 m) sin(nz) in sine form. C) Express the function y3= (4 m) cos(-x )-(2 m) sin(-x
Consider the following initial value problem, in which an input of large amplitude and short duration...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: z" + 167°1 = 478(t – 5), 7(0) = 0, z'(0) = 0. In the following parts, use h(t - c) for the Heaviside function hc(t) if necessary. a. Find the Laplace transform of the solution. [{r(t)}(s) = bir b. Obtain the solution z(t). z(t) = c. Express the solution as a piecewise-defined function and think about...
5. For the previous problem write an equation of its oscillatory motion using a sine or...
5. For the previous problem write an equation of its oscillatory motion using a sine or cosine function and assuming that the object starts as indicated above. Find the position and velocity of the object at time = 0.26 sec. (You have to determine to use a cosine of sine function and the initial angle based on the initial conditions given in the previous problem). 4. A mass of 1.80 kg is attached to a horizontal spring with a spring...
Given The partial graph of the cosine function below has a minimum post -2 nd a...
Given The partial graph of the cosine function below has a minimum post -2 nd a maximum point at C ) as shown below. The equation of the function can be expressed in the form acos -c))+d. ...c.d w . a) Draw the midline on the graph. b) What is the amplitude of the graph? c) What is the period of the graph? d) What is the value of b in the above equation? e) What is the phase shift...
= Problem #2: The function f(x) sin(4x) on [0:1] is expanded in a Fourier series of...
= Problem #2: The function f(x) sin(4x) on [0:1] is expanded in a Fourier series of period Which of the following statement is true about the Fourier series of f? (A) The Fourier series of f has only cosine terms. (B) The Fourier series of f has neither sine nor cosine terms. (C) The Fourier series of f has both sine and cosine terms. (D) The Fourier series of f has only sine terms.
(2) Consider the function f(x)- 1 (a) Find the Fourier sine series of f (b) Find...
(2) Consider the function f(x)- 1 (a) Find the Fourier sine series of f (b) Find the Fourier cosine series of f. (c) Find the odd extension fodd of f. (d) Find the even extension feven of f. (e) Find the Fourier series of fod and compare it with your result -x on 0<a < 1. in (a) (f) Find the Fourier series of feven and compare it with your result in (b)
I need help with the following problem: Consider a periodic signal !(t), with period T, such...
I need help with the following problem:
Consider a periodic signal !(t), with period T, such that !(t) 0, 圹 From Example 2.3.1 of the class notes, the nth Fourier coefficient of r(t) is given by in012... a) Use Fourier series, and the symmetry of the sinc function, to express r(t) in terms of cosine functions. Do we also need sine functions in this representation? b) Suppase that is a signal with Fourier transform S Find and plot the Fourier...
Problem 2. Consider the function plotted below. A) What is the amplitude of this function? B) What is (approximately) the wavelength of this function? C) What is (approximately) the spatial frequency of this function? D) Express (approximately) this function in sine form. E) Express (approximately) this function in cosine form. 0. -2 -5 -2.5 0. 2.5 a (m)
(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...
Problem 4 -π/3) in quadrature form. 2π A) Express the function Y1 = (2 m) sin( 5-x B) Express the function y3=(4m)cos(10-)-(2m) sin( nx) incosine form. 10 in sine form. C) Express the function y3= (4 m) cos(nz)-(2 m) sin(nz) in sine form. C) Express the function y3= (4 m) cos(-x )-(2 m) sin(-x
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: z" + 167°1 = 478(t – 5), 7(0) = 0, z'(0) = 0. In the following parts, use h(t - c) for the Heaviside function hc(t) if necessary. a. Find the Laplace transform of the solution. [{r(t)}(s) = bir b. Obtain the solution z(t). z(t) = c. Express the solution as a piecewise-defined function and think about...
5. For the previous problem write an equation of its oscillatory motion using a sine or cosine function and assuming that the object starts as indicated above. Find the position and velocity of the object at time = 0.26 sec. (You have to determine to use a cosine of sine function and the initial angle based on the initial conditions given in the previous problem). 4. A mass of 1.80 kg is attached to a horizontal spring with a spring...
Given The partial graph of the cosine function below has a minimum post -2 nd a maximum point at C ) as shown below. The equation of the function can be expressed in the form acos -c))+d. ...c.d w . a) Draw the midline on the graph. b) What is the amplitude of the graph? c) What is the period of the graph? d) What is the value of b in the above equation? e) What is the phase shift...
= Problem #2: The function f(x) sin(4x) on [0:1] is expanded in a Fourier series of period Which of the following statement is true about the Fourier series of f? (A) The Fourier series of f has only cosine terms. (B) The Fourier series of f has neither sine nor cosine terms. (C) The Fourier series of f has both sine and cosine terms. (D) The Fourier series of f has only sine terms.
(2) Consider the function f(x)- 1 (a) Find the Fourier sine series of f (b) Find the Fourier cosine series of f. (c) Find the odd extension fodd of f. (d) Find the even extension feven of f. (e) Find the Fourier series of fod and compare it with your result -x on 0<a < 1. in (a) (f) Find the Fourier series of feven and compare it with your result in (b)
I need help with the following problem:
Consider a periodic signal !(t), with period T, such that !(t) 0, 圹 From Example 2.3.1 of the class notes, the nth Fourier coefficient of r(t) is given by in012... a) Use Fourier series, and the symmetry of the sinc function, to express r(t) in terms of cosine functions. Do we also need sine functions in this representation? b) Suppase that is a signal with Fourier transform S Find and plot the Fourier...
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