8.A certain vibrating system satisfies the equation u″ + γu′ + u = 0. Find the value of the damping coefficient γ for which the quasi-period of the damped motion is 50% greater than the period of the corresponding undamped motion.

Q: 14. The position vector of a particle of mass 2kg is given as a function of time by: I r= = (4i + 2t…

A: Solution:-

Q: A particle is oscillating about a central point such that its displacement x (centimetres) at any…

A: Given that the displacement x at any time t is modeled by the equation x=sint+cost+cost-π3 for t≥0.…

Q: For each case, your answer should include: a classification of the stationary point, if required, a…

A: As per the question, we analyze the small-amplitude oscillation of a pendulum with an angle θ(t)…

Q: (a) By considering numerical differentiation aT_T(x,1+1)-7(x,1), deduce that the temperature…

A:

Q: 92 that the elect ric potential prove -5x V = e Cos 13y sinh 12 Z achieves the Laplace equation اثبت…

A:

Q: V3.6.4 The movement of a particle is given by the equations ze, yet and z=0 for its coordinates,…

A: The equations that describe the motion of a moving particle are given by x=et2, y=e-t2 and z=0. In…

Q: dY 1 dt -1 a

A: This is a problem of stability Theory, a system of the differential equations.

Q: 8. feet. The mass is initially released from rest from a point 3 feet below the equilibrium…

A:

Q: 1.11 Determine if the following equations are linear or nonlinear: a. y = 4 15x 3 b. y = 3x X c. y =…

A: We have to determine following equation is linear or not. Note:- These are multiple sub parts we can…

Q: Draw approx. solution for the directional field for the first order with the initial condition y(0)…

A: Given directional field:

Q: The motion of a mass-spring system with damping is governed by y'' (t) + by' (t) +9y(t) = 0; y(0) =…

A:

Q: Consider the logistic equation in the form P'(t) = CP − P2. C = 4 Draw the directional field.…

A: Below given clear explanation

Q: Calculate the velocity, speed, and acceleration of the given paths. (a) x(t) = (t sin(t), t cos(t),…

A:

Q: 1) Write the given second order equation as its equivalent system of first order equations. u"…

A:

Q: The displacement in simple harmonic mo- tion is a maximum when the 1. velocity is a maximum. 2.…

A: The displacement in simple harmonic mo tion is a maximum when the ............

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

A:

Q: Find the differential equation of the family plane curves described. Draw atleast three members of…

A:

Q: (19) The direction field pictured below is for the differential equation y'=(x-2)(y² – 9). a) Sketch…

A: according to our guidelines we can answer only three subparts and rest can be reposted.

Q: 6. Simplified equations for an electric motor can be given O"(t) + 20'(t) = u(t) where e(t) is the…

A: Given equation for an electric motor is θ''t+2θ't=ut

Q: Q.2) Find the orthogonal trajectories of the family of curves e*(x sin y– y cos y) = c

A: 2 Given family of curves is e−xxsiny−ycosy=c. We have to find the orthogonal trajectories of the…

Q: (1.) Calculate the proper distance between two free particles, one at the origin of a coor- dinate…

A:

Q: Plot a number of isoclines and construct a direction field for the equation dy dy y = x- dx dx If…

A: Given the differential equation y=xdydx+dydx2.…

Q: As a spring ages, its spring "constant" decreases in value. One such model for a mass-spring system…

A: Given that x''t+3x't+3e−txt=0 and, x0=3, x'0=0 To find the first four nonzero terms in a power…

Q: 3. (Free-driving force, damped mass-spring system). Recall that the underdamped motion of the system…

A:

Q: 10. Solve: (2st +1 kds – 3s° dt = 0, s(-1)=1 a. 8st' = (s -t) – t)² c. 8st = (t – s) 3 а. 8st3 b.…

A:

Q: A classical equation of mathematics is Laplace's equation, which arises in both theory and…

A: The given function is; u=e6x cos(-6y)