a)Determine the phase constant ϕ (−π≤ϕ≤π) in x=Acos(ωt+ϕ) if, at t=0, the oscillating mass is at...
a)Determine the phase constant ϕ (−π≤ϕ≤π) in x=Acos(ωt+ϕ) if, at t=0, the oscillating mass is at x=A.
b)Determine the phase constant ϕ (−π≤ϕ≤π) in x=Acos(ωt+ϕ) if, at t=0, the oscillating mass is at x=1/2A.
c)Determine the phase constant ϕ (−π≤ϕ≤π) in x=Acos(ωt+ϕ) if, at t=0, the oscillating mass is at x=−1/2A.
d)Determine the phase constant ϕ (−π≤ϕ≤π) in x=Acos(ωt+ϕ) if, at t=0, the oscillating mass is at x=A/√2
Homework Answers
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a)Determine the phase constant ϕ
(−π≤ϕ≤π) in
x=Acos(ωt+ϕ) if, at
t=0, the oscillating mass is at...
Define x(t) as x(t) = 2 cos(ωt + 5) + 8 cos(ωt + 9) + 4...
Define x(t) as x(t) = 2 cos(ωt + 5) + 8 cos(ωt + 9) + 4 cos(ωt) where the phases have units of radians. Express x(t) in the form x(t) = Acos(ωt + ϕ). Use a calculator to add the complex phasors to obtain the answer. Explain your answer by giving a vector diagram of the phasors.
I. A mass oscillating on a spring has a phase constant φο- rad, an angular frequency...
I. A mass oscillating on a spring has a phase constant φο- rad, an angular frequency w = π rad/s and an amplitude A-4.0 cm. (a) Draw a circle of radius 4.0 cm and indicate on the circle the phase constant, if the simple harmonic motion is well-described by the r-component of uniform circular motion with the same angular speed as this angular frequency. /4 (d) Sketch a graph of r versus t. Include two periods in your time axis...
I. A mass oscillating on a spring has a phase constant φο- rad, an angular frequency...
I. A mass oscillating on a spring has a phase constant φο- rad, an angular frequency w = π rad/s and an amplitude A-4.0 cm. (a) Draw a circle of radius 4.0 cm and indicate on the circle the phase constant, if the simple harmonic motion is well-described by the r-component of uniform circular motion with the same angular speed as this angular frequency. /4 (d) Sketch a graph of r versus t. Include two periods in your time axis...
1 1 2 79.7% 1. A mass oscillating on a spring has a phase constantad, an...
1 1 2 79.7% 1. A mass oscillating on a spring has a phase constantad, an angular frequency w = π rad/s and an amplitude A 4.0 cm. (a) Draw a circle of radius 4.0 cm and indicate on the circle the phase constant, if the simple harmonic motion is well-described by the r-component of uniform čircular motion with the same angular speed as this angular frequency. /4 (b) Write an expression for the position, r(t), of the mass as...
The position of a particle is given by the expression x = 4.00 cos (6.00πt +...
The position of a particle is given by the expression x = 4.00 cos (6.00πt + π), where x is in meters and t is in seconds. (a) Determine the frequency. Incorrect: Your answer is incorrect. How is the frequency related to the angular frequency? Hz (b) Determine period of the motion. Incorrect: Your answer is incorrect. How is the period related to the frequency? s (c) Determine the amplitude of the motion. Incorrect: Your answer is incorrect. The amplitude...
In-Class Assignment 2. The figure shows a position-versus-time graph for an oscillating mass m = 0.5...
In-Class Assignment 2. The figure shows a position-versus-time graph for an oscillating mass m = 0.5 kg. x (cm) 20 10 0 -10 -20 I(s) 4 a. Determine the period of the motion. b. Determnine the angular frecquemcy of the motion c. Determine the amplitude of the motion. d. Determine the phase constant of the motion. e. Determine the maximum speed of the mass. f. Determine the maximum acceleration of the mass. g. Determine the total energy of the system....
A. The position of a 45 g oscillating mass is given by x(t)=(2.0cm)cos(10t), where t is...
A. The position of a 45 g oscillating mass is given by x(t)=(2.0cm)cos(10t), where t is in seconds. Determine the velocity at t=0.40s. B. Assume that the oscillating mass described in Part A is attached to a spring. What would the spring constant k of this spring be? C. What is the total energy E of the mass described in the previous parts?
The sinusoidal function represented in this plot is in the form y=A*cos(ωt+ϕ). Please help on parts...
The sinusoidal function represented in this plot is in the form
y=A*cos(ωt+ϕ). Please help on parts a-c.
6 4 2 2 3 4 time Part a What is A? Enter answer here 0 of 3 attempts used CHECK ANSWER Part b What is w? Enter answer here 0 of 3 attempts used CHECK ANSWER Part c What is ? There are many answers possible after all you can always add or subtract π from the argument of a cos function...
Let x(t) = Acos(27/0t + ?) where fo is a given constant, A is a Rayleigh...
Let x(t) = Acos(27/0t + ?) where fo is a given constant, A is a Rayleigh random variable with ? is a uniformly distributed random variable on [0, 2n, and A and ? are statistically independent. a) Find the mean E[X (t)h b) Find the autocorrelation function E(X(t)X(t+)). c) Is (X(t)) wide-sense stationary? d) Find the power spectral density Sx(f)
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The input to an op amp-based low-pass filter with a cutoff frequency of 500 Hz and a passband gain of 8 is 2.8cosωt V. Part A Part complete Suppose the power supplies are ±Vcc. What is the smallest value of Vcc that will still cause the op amp to operate in its linear region? Express your answer to three significant figures and include the appropriate units. Vccmin = 22.4 V (Correct) Part B Find the output voltage when ω=ωc.Suppose that...
I. A mass oscillating on a spring has a phase constant φο- rad, an angular frequency w = π rad/s and an amplitude A-4.0 cm. (a) Draw a circle of radius 4.0 cm and indicate on the circle the phase constant, if the simple harmonic motion is well-described by the r-component of uniform circular motion with the same angular speed as this angular frequency. /4 (d) Sketch a graph of r versus t. Include two periods in your time axis...
I. A mass oscillating on a spring has a phase constant φο- rad, an angular frequency w = π rad/s and an amplitude A-4.0 cm. (a) Draw a circle of radius 4.0 cm and indicate on the circle the phase constant, if the simple harmonic motion is well-described by the r-component of uniform circular motion with the same angular speed as this angular frequency. /4 (d) Sketch a graph of r versus t. Include two periods in your time axis...
1 1 2 79.7% 1. A mass oscillating on a spring has a phase constantad, an angular frequency w = π rad/s and an amplitude A 4.0 cm. (a) Draw a circle of radius 4.0 cm and indicate on the circle the phase constant, if the simple harmonic motion is well-described by the r-component of uniform čircular motion with the same angular speed as this angular frequency. /4 (b) Write an expression for the position, r(t), of the mass as...
In-Class Assignment 2. The figure shows a position-versus-time graph for an oscillating mass m = 0.5 kg. x (cm) 20 10 0 -10 -20 I(s) 4 a. Determine the period of the motion. b. Determnine the angular frecquemcy of the motion c. Determine the amplitude of the motion. d. Determine the phase constant of the motion. e. Determine the maximum speed of the mass. f. Determine the maximum acceleration of the mass. g. Determine the total energy of the system....
The sinusoidal function represented in this plot is in the form
y=A*cos(ωt+ϕ). Please help on parts a-c.
6 4 2 2 3 4 time Part a What is A? Enter answer here 0 of 3 attempts used CHECK ANSWER Part b What is w? Enter answer here 0 of 3 attempts used CHECK ANSWER Part c What is ? There are many answers possible after all you can always add or subtract π from the argument of a cos function...
Let x(t) = Acos(27/0t + ?) where fo is a given constant, A is a Rayleigh random variable with ? is a uniformly distributed random variable on [0, 2n, and A and ? are statistically independent. a) Find the mean E[X (t)h b) Find the autocorrelation function E(X(t)X(t+)). c) Is (X(t)) wide-sense stationary? d) Find the power spectral density Sx(f)
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