Problem 6. Consider the function y=(2m) sin ((10/s) t+π/4). Indicate whether each of the following waveforms...
- Problem 6. Consider the function y2 m) sin ((10/s) t+π/4). lndicate whether each of the following waveforms is equivalent to y? Briefly justify your answers 1. (2 m) cos(10/s)t+/4) 2. (2 m) cos( (10/s)t+3 T/4) 3. (2m) cos( (10/s)t -/4) 4. (2 m) sin((10/ s) t + π/4 + 4 π) 5.-(2 m) sin ((10/s) t + π /4-3r) 6. (-2m) cos((10/s) t + 12n/4) 7. (v ฐ m) [cos((10/s) t) + sin((10/s) t)] 8. (2 m) cos ((-10/s)...
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
a. Find the curvature of the curve r(t)- (9+3cos 4t)i-(6+sin 4t)j+10k. o. Find the unit tangent vector T and the principal normal vector N to the curve -π/2<t<π/2. r(t) = (4 + t)i-(8+In(sect))j-9k, Find the tangential and normal components of the acceleration for the curve r(t)-(t2-5)i + (21-3)j +3k. a. Find the curvature of the curve r(t)- (9+3cos 4t)i-(6+sin 4t)j+10k. o. Find the unit tangent vector T and the principal normal vector N to the curve -π/2
Define f: R2R3 b f(s,t) (sin(s) cos(t), sin(s) sin(t), cos(s)). (a) Describe and draw the image of f. (b) Proeve i.baat uts dilikur#xot.ial le. (c) Find the Jacobian matrix of f at (π/3, π/4) (d) Describe and draw the im age of Df(m/3, π/4). (e) Draw the image of Df(n/3, π/4) translated by f(n/3, π/4). (f) Describe the relationship between the image of f and the translated image of Df(T/3,/4) in nart (e Define f: R2R3 b f(s,t) (sin(s) cos(t),...
Question 4 (2+4+4+1+4 = 15 marks) Consider the function y = 4 sin (2x-π) for-r below to sketch the graph of y. x < π. Follow the steps (a) State the amplitude and period in the graph of this function 4 sin (22-9 ) for-r (b) Solve y π to find the horizontal intercepts x (a-intercepts) of the function. (c) Find the values of x for-π π for which the maximum. and the x minimum values of the function occur...
(a) xi (t) =4(sin(31) + cos(3t)] (b) x2(t) = sin(41) 1.18 For each of the following functions, indicate if it exhibits even symmetry, odd symmetry, or neither one. (a) Xi (t) = 1-e-2t (b) x2(t) = 1-e-2t2 1.19 Generate plots for each of the following step-function waveforms over the time span from-5 s to +5 s. (a) xi (t)=-611 (t + 3) (b) x2(t) = 1011(1-4) (c) x3(t) = 411 (t + 2) _ 411 (1-2)
1)a)The acceleration of a car is given by the function a(t) = sin(t) m / s² at time t s. The average acceleration for 0 ≤ t ≤ π s is _____ m / s². Round your answer to two decimal places. b) The acceleration is given by a(t) = 4t at time t s. The initial position is 1 m, and, the initial velocity is 3 m / s. At time t = 4 s, the position is _____...
Consider the following transfer function: [mark 25%] 4. Y(s) U(s) 5s1 2 G(s) (3) a. If U(s) b. If U (s) (1 - e-)/s, what is the output whent » co? If u(t) 6(t) that is, the unit impulse at t 0, what is the output when t > co? d. Ifu(t) sin(4t), what is y(t) when t co? 3/s, what is the value of the output when t 10? C. Consider the following transfer function: [mark 25%] 4. Y(s)...
The given input signal for 2.7.2 is: x(t) = 3 cos(2 π t) + 6 sin(5 π t).Plz explain steps.Given a causal LTI system described by the differential equation find \(H(s),\) the \(\mathrm{ROC}\) of \(H(s),\) and the impulse response \(h(t)\) of the system. Classify the system as stable/unstable. List the poles of \(H(s) .\) You should the Matlab residue command for this problem.(a) \(y^{\prime \prime \prime}+3 y^{\prime \prime}+2 y^{\prime}=x^{\prime \prime}+6 x^{\prime}+6 x\)2.7.2 The signal \(x(t)\) in the previous problem is...
A string oscillates according to the equation y´ = (0.529 cm) sin[(π/6.0 cm-1)x] cos[(42.4 π s-1)t]. What are the (a) amplitude and (b) speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the transverse speed of a particle of the string at the position x = 1.64 cm when t = 1.18 s?