Suppose a damping force affects the vibration of a spring so that the displacement of the string is given by y-e (cos 2t + 9 sin 21). Find the average value of y on the interval from t-0 to - x. Round your answer to three decimal places. -81

Q: 7. A mass weighing 3 lb stretches a spring 3 in. If the mass is pushed upward, contracting the…

A: Given that: Weight = 3 lb Spring stretched = 3 in. Initial position, y(0) = -1 in = -1/12 ft…

Q: 10. The slope of the tangent line to the curve y(cos x)+e' =5 at the point where x= is (5+In 5) In5…

A: The slope of a  tangent line of a curve at any point will be equal to the slope of the curve at that…

Q: An alternating current E(t)=120sin(12t) has been running through a simple circuit for a long time.…

A: Here, L=0.28 H R=9 ohms C= 0.04 F

Q: A damping force affects the vibration of a spring so that the displacement of the spring is given by…

A: Given y=e-3t(cos6t+2sin6t)

Q: 1 f(t) dt = ln(x) cos(x) + /. e* f(t) dt, find f(x). You may find FTC 1 useful. n(3) Given sin(3)

A: The solution are next step

Q: Consider the forced linear harmonic oscillator y" + w?y = cos wt where the frequency W = 4 Find a…

A: We are given that y''+ω2y=cosωtwhich can be written as (D2+ω2)y=cosωt.We have to find particular…

Q: (a) A mass weighing 2 lb stretches a spring 6 in. If the mass is pulled down an additional 3 in and…

A: Consider the provided question, A mass weighing 2 lb stretches a spring 6 in. If the mass is pulled…

Q: The approximation of I = S cos (x² + 5) dx using simple Simpson's rule is: 0.54869 "-0.93669 This…

A: We have to solve by Using Simpsons 1/3 rule .

Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j + 12t k at a distance 26p units along the…

A:

Q: Suppose the position function of a particle is given by r(t)=(√3 sin(t), t-2, √3 cos(t)). If the…

A:

Q: 13. Find the value of t in the given interval at which the given curve is not smooth. r(t)=(5cost-…

A: Given curve: r(t)=5cos t-cos 5t, 5sin t-sin 5tt interval: π4,3π4

Q: A particle travels along the x-axis such that its position is given by x(t) = velocity of the…

A:

Q: Suppose a mass-spring system exhibits damped harmonic motion, modeled by the function f (t) =…

A:

Q: t+0 tan3 2t t+0 sin 10t 10.1 letcariorg line horizontal? At what points on the curve y = sin x + cos…

A:

Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: (b) Starting with the voltage divider rule, show that the power transmission coefficient T of an RC…

A:

Q: The exact value of the slope of the tangent line to the graph of the curve r = 5 + 4 cos(0), at e =…

A:

Q: The velocity v and time t are related by the first order differentia pelow. Find the velocity att =…

A: Here we have,  dvdt-15vtant5=20 given v(0)=1. Where v= velocity,  t = time

Q: а. A particle moves along a straight line with an acceleration of a = 4 sin m/s². If the…

A: As you haven't mentioned so I'm doing only part (a).  a) i. The acceleration of the particle after 2…

Q: A particle moves along the x-axis with position function a (t) = 4 sin for 0 <t< 4n where t is…

A:

Q: The displacement of a structure is defined by the following equation for a damped oscillation: y = 7…

A: Newton-Raphson method uses the following formula to perform the iterations. xn+1=xn-f(xn)f'(xn) The…

Q: 4. The position of a particle at time t is given by x(t) = 5+4 sin(t) y(t) = 2 − 4 cos(t) 0<t</ (a)…

A: This is a problem of parametric curve and Integration.

Q: A yoyo bounces up and down in the vertical direction with its acceleration after tt seconds given by…

A: d^2y/dt^2 = a(t)

Q: 3. Find the position and velocity of the particle if its acceleration is a(t)=-cos(t)i – sin(t)j…

A:

Q: A particle moves along the x-axis with velocity given by v(t) = 2 sin (2t) for time t>0. If the…

A:

Q: Consider the position function s(t) = 3 sin t that describes a block bouncing vertically on a…

A:

Q: A particle is moving along the x-axis with a velocity of v (t) = 8 cos (). The particle is at x=2…

A:

Q: The displacement of a structure is defined by the following equation for a damped oscillation y =…

A: By this method 1st we will find an interval where roots can lie and then use xn+1=xn-f'(xn)f(xn) to…

Q: A weight on a spring is bobbing up and down. Its height above the ground at time t is h(t) = 5 +…

A:

Q: A particle moves along a straight line with an acceleration of a = 4 sin 4 m/s?. If the displacement…

A: a=dvdt v=dx/dt sin pi=0 cos pi=-1

Q: Find the average power of the signal: x(t) : = cos x + sin x (-7/4, 0) (7n/4, 0)

A: From the given graph, it is observed that the period of function is T0=7π4--π4=2π. Compute the…

Q: Use the rules to get a formula for the derivative of m(t) = In(t? + 3) vt? + 3 with respect to t Use…

A: Here we will apply basic rules of derivatives and chain rule of differentiation.

Q: Faraday's law characterizes the voltage drop across an inductor such as Given that di V = L dt 1 di…

A:

Q: A damping force affects the vibration of a spring so that the displacement of the spring is given by…

A:

Q: The surface of a water wave is describedby y = 5(1 + cos x), for -∏ ≤ x ≤∏, where y = 0corresponds…

A: Given- y=51+cosx and consider the figure, To find- The average height of the wave above the trough…

Q: onsider the position function s(t) =8 sin 5t that describes a block bouncing vertically on a spring.…

A:

Q: A sinewave, f(t) is zero and increasing at t = 1ms and the succeeding positive maximum of 8.5 occurs…

A: Given that Zero at 1ms means lag by 1 ms. Max at 7.5 ms. Therefore,  T4=-1+7.5T4=6.5T=26 ms So,…

Q: A particle moving along a curve in the xy-plane has position (x(t), y(t)), at time t > 0 where v(t)…

A: solution:-v(t)=-2ln(t2+8), -10e-8tcos5tat t=5v(0)=-2ln(52+8), -10e-85cos55       =-2ln33,…

Q: Q2) For the circuit in the figure, the capacitance is 0.5, the resistor is linear with v-i…

A: Electric current is measured as number of charge passing through a point per unit time, therefore…

Q: The height (in centimeters) at time t (in seconds) of a small mass oscillating at the end of a…

A:

Q: 17. The displacement of a structure is defined by the following equation for a damped oscillation: y…

A: here the calculations are done taking t as x so just the variable change nothing different. Here…

Q: A damping force affects the vibration of a spring so that the displacement of the spring is given by…

A:

Q: A mass attached to a vertical spring has position function given by 8(t) = 4 sin(4t) where t is…

A:

Q: Q3: Find F.T of the pulse sine wave shown in fig. below: S(1) A sin at Ans. (e-2ja – 1)

A: Use the sine functions Fourier equation and then integrate it with limits of the graph which are 0…

Q: A mass of 1 kg is attached to a spring and a damper, set in motion, and observed to move as x(t) = 3…

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Q: Find the first order derivative for the following: cot(e(3•Z)t) sin(z•t²) S = t5

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Q: Find the length of the curve defined by the following function for 0 <t < 2n. 7(t) = (– cos 2t)i +…

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Q: 2. The speed of a particle at an arbitrary time t is given by || V(4t - 1) +sin? rt. Then V.d at t =…

A:

Q: The displacement from equilibrium of an object in harmonic motion on the end of a spring is y =…

A: We have, the displacement from equilibrium of an object in harmonic motion on the end of a spring as…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.