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Find the time form x(,) = 4e'" sin(ar) , where identity 2. where the displacement is...
Given that sin x = 3/4, use a Pythagorean identity to find cos x in simplest...
Given that sin x = 3/4, use a Pythagorean identity to find cos x in simplest radical form.
solve it by using matlab Question 2) (2.5 points) Examine the following trigonometric identity: sin'(x) =...
solve it by using matlab
Question 2) (2.5 points) Examine the following trigonometric identity: sin'(x) = (3 sin(a) – sin(3.c)) Verify that this identity is valid. To do so, define a variable x as x = 84 (in degrees!). Compute the left and right sides of the identity and assign them to variables p2left and p2right. Because x is in degrees, make sure you are using the correct trig function! Use the help function if you are unsure. Question 1)...
2. Use what you know about complex numbers in polar form to derive the identity sin(a...
2. Use what you know about complex numbers in polar form to derive the identity sin(a + b) = sin(a) cos(b) + cos(a) sin(b)
2./(20 pts) A certain cam function is given in the following form: d'xce. c1-sin(f1-9) where x...
2./(20 pts) A certain cam function is given in the following form: d'xce. c1-sin(f1-9) where x is the displacement of the follower and θ is the angular displacement of the input shaft; CI is a constant related to the displacement range of x and f1 is determined by the portion of input shaft rotation to complete the rise portion of cam motion. Assume that the rise part of the motion is completed in, Orie -0.25 rev, so that fi-4. Furthermore,...
4. Find the general solution to the system x' = Ar, where A is as specified...
4. Find the general solution to the system x' = Ar, where A is as specified below. Make sure to write the solution in purely real form. 1 1 0 (a) A= ( -4 3 ) (1 -5 ) (b) A=1 (1 -3) 1 1 0 0 (c) A= | -2 1 2 1 -2 -2 1 ( -5 -3 (d) A= ( 7 ) 31 (You can skip part (d) as it is from $3.7.)
Let Y-ar+b (a) Find the mean and variance of Y in terms of the mean and variance of X b) Evaluate...
Let Y-ar+b (a) Find the mean and variance of Y in terms of the mean and variance of X b) Evaluate the mean and variance ofY if Xhas the following PDF: (a)-ele (c) Evaluate the mean and variance of Y if Xis the Gaussian random variable with mean 0 and variance d) Evaluate the mean and variance of Yif X-bcos 2U) where U is a uniform random variable in of 1 the unit interval.
Let Y-ar+b (a) Find the mean...
Let's consider a function described in terms of its displacement y(x,t) at t 0 by: where a, b and e are positive constants a) Write an expression for this wave profile, having a speed in the nega...
Let's consider a function described in terms of its displacement y(x,t) at t 0 by: where a, b and e are positive constants a) Write an expression for this wave profile, having a speed in the negative x-direction, as a function of position and time (b) Sketch the profile of the wave at t-0 s and t 2 s if v1 m/s (c) Determine if the following functions describe a travelling wave: (i) vr,t) (ar+ bt c), where a, b...
-2 points SerCP111 3 OP02 Notes O As (a) Suppose that the displacement x of an...
-2 points SerCP111 3 OP02 Notes O As (a) Suppose that the displacement x of an object is related to time t according to the expression x-Br2 What are the dimensions of 87 O LT O LIT2 (b) Suppose the displacement x of another object is related to time t according to x -A sin(2ft), where A and fare constants. What are the dimensions of A? (Hint: A trigonometric function appearing in an equation must be dinensionless.) T/L
Torsional vibration of a shaft is governed by the wave equation, = 16 where (x,t) is the angular displacement (angle of...
Torsional vibration of a shaft is governed by the wave equation, = 16 where (x,t) is the angular displacement (angle of twist) along the shaft, ar is the distance from the end of the shaft and t is time. For a shaft of length 2T that supported by frictionless b end, the boundary conditions are 0r(0,t) = 0x(2T, t) = 0, t> 0. Suppose that the initial angular displacement and angular velocity are (x,0) = 6 cos(x), Ot(x,0) =3+2 cos(42),...
Verify that the equation is an identity. sin (x-y) tan x- tany sin (x+y) tanx +...
Verify that the equation is an identity. sin (x-y) tan x- tany sin (x+y) tanx + tany Which of the following statements verifies that the equation is an identity? O A A tan x-tany tanx+ tany sin?(x - y) V1- cos? (x-y) 11 - cos? (x + y) sin(x - y) sin (x+y) O B. sin (x-y) sin cosy - cos x siny sin x- cos y tan x-tany sin (x+y) sin x cos y + cos x siny sin...
solve it by using matlab
Question 2) (2.5 points) Examine the following trigonometric identity: sin'(x) = (3 sin(a) – sin(3.c)) Verify that this identity is valid. To do so, define a variable x as x = 84 (in degrees!). Compute the left and right sides of the identity and assign them to variables p2left and p2right. Because x is in degrees, make sure you are using the correct trig function! Use the help function if you are unsure. Question 1)...
2. Use what you know about complex numbers in polar form to derive the identity sin(a + b) = sin(a) cos(b) + cos(a) sin(b)
2./(20 pts) A certain cam function is given in the following form: d'xce. c1-sin(f1-9) where x is the displacement of the follower and θ is the angular displacement of the input shaft; CI is a constant related to the displacement range of x and f1 is determined by the portion of input shaft rotation to complete the rise portion of cam motion. Assume that the rise part of the motion is completed in, Orie -0.25 rev, so that fi-4. Furthermore,...
4. Find the general solution to the system x' = Ar, where A is as specified below. Make sure to write the solution in purely real form. 1 1 0 (a) A= ( -4 3 ) (1 -5 ) (b) A=1 (1 -3) 1 1 0 0 (c) A= | -2 1 2 1 -2 -2 1 ( -5 -3 (d) A= ( 7 ) 31 (You can skip part (d) as it is from $3.7.)
Let Y-ar+b (a) Find the mean and variance of Y in terms of the mean and variance of X b) Evaluate the mean and variance ofY if Xhas the following PDF: (a)-ele (c) Evaluate the mean and variance of Y if Xis the Gaussian random variable with mean 0 and variance d) Evaluate the mean and variance of Yif X-bcos 2U) where U is a uniform random variable in of 1 the unit interval.
Let Y-ar+b (a) Find the mean...
Let's consider a function described in terms of its displacement y(x,t) at t 0 by: where a, b and e are positive constants a) Write an expression for this wave profile, having a speed in the negative x-direction, as a function of position and time (b) Sketch the profile of the wave at t-0 s and t 2 s if v1 m/s (c) Determine if the following functions describe a travelling wave: (i) vr,t) (ar+ bt c), where a, b...
-2 points SerCP111 3 OP02 Notes O As (a) Suppose that the displacement x of an object is related to time t according to the expression x-Br2 What are the dimensions of 87 O LT O LIT2 (b) Suppose the displacement x of another object is related to time t according to x -A sin(2ft), where A and fare constants. What are the dimensions of A? (Hint: A trigonometric function appearing in an equation must be dinensionless.) T/L
Torsional vibration of a shaft is governed by the wave equation, = 16 where (x,t) is the angular displacement (angle of twist) along the shaft, ar is the distance from the end of the shaft and t is time. For a shaft of length 2T that supported by frictionless b end, the boundary conditions are 0r(0,t) = 0x(2T, t) = 0, t> 0. Suppose that the initial angular displacement and angular velocity are (x,0) = 6 cos(x), Ot(x,0) =3+2 cos(42),...
Verify that the equation is an identity. sin (x-y) tan x- tany sin (x+y) tanx + tany Which of the following statements verifies that the equation is an identity? O A A tan x-tany tanx+ tany sin?(x - y) V1- cos? (x-y) 11 - cos? (x + y) sin(x - y) sin (x+y) O B. sin (x-y) sin cosy - cos x siny sin x- cos y tan x-tany sin (x+y) sin x cos y + cos x siny sin...
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