1. Derive the equation of velocity and acceleration from this equation of displacement x=K sin (wt) in simple harmonic motion.

Q: 7. A spring is stretched 200 mm by a 15-kg block. If the block is displaced 100 mm downward from its…

A:

Q: What is the equation of the line tangent to the curve ev + cos(x) = 1 at the point (,0*? Y = 0 A B…

A:

Q: 1. If an object moves with velocity v(t) = sin(t) + 3t and begins at position p(0) = 0, find the…

A:

Q: 1) Find the equations of the lines that are tangent to Y = 0.5(sin 2t) at the origin the curve COs…

A:

Q: A particle P moves with constant acceleration (-4i+2j)ms. At time t= 0 seconds, Pis moving with…

A:

Q: A particle moves along a straight line with velocity function  v(t) = sin t - cos t and its initial…

A: Given that a particle moves along a straight line with velocity function vt=sint-cost and its…

Q: Ex. 1. A shot of mass m, is fired from a gun of mass m2 with velocity v relative to the gun; show…

A:

Q: 7. The velocity of an object traveling along a straight line is v(t) = cos(t) + 4t + 1 meters per…

A: Solved below

Q: 4. A 10-kg mass is attached to a spring having a spring constant of 140 N/m. The mass is started in…

A:

Q: 1) Find -(d(PE))/dx in order to find the force acting on the object. (from the equation PE=(1/2)k^2)…

A: Given:

Q: 2. A Ferris wheel of diameter 18.5 m rotates at a rate of 9.2 rad/s. If passengers board the lowest…

A:

Q: Find the extremal of the functions using Euler's equation. [²(x² + y² (y2 + y² + 2ye*)dx, y (0) = 0,…

A:

Q: A mass weighing l16 pounds stretches a spring feet. The mass is initially released from rest from a…

A: Formula: Let m be the mass attached, k be the spring constant and β be the positive damping constant…

Q: 9.Show that the period of motion of an undamped vibration of a mass hanging from a vertical spring…

A:

Q: Give the number of complete oscillations that will occur over 1 minute for a mass- spring system…

A:

Q: 11. Find an equation of the tangent plane to the surface T+VG+vz = 4 at the point P(4, 1,1).

A: we have to find the tangent plane on the given surface x+y+z=4 at the point P(4, 1, 1)

Q: The slope of the tangent to the curve r = 3 sin 40 at 0 = 0 is %3D Şelect one: O a. -1 3D1 O b. 0 C.…

A:

Q: 6) A weight oscillates in a vertical motion according to the position function y(f) = -5 cos t.…

A: Acceleration for position function yt=-5cost is d2ydt2. Calculate double derivative d2ydt2 and…

Q: After a mass weighing 10 pounds is attached to a 5-foot spring, the spring measures 7 feet. This…

A: Let m be the mass , k be spring constant and  β be positive damping constant. The Newton's second…

Q: 1.)Supposed that a mass weighing 10 lbs. stretches a spring 2 inches. If the mass is displaced…

A:

Q: (a) Find the equation of the tangent line to y = lnx at x = 1. (b) Use the tangent line to calculate…

A: solve the following

Q: Can anything be said about the tangent lines to the curves y = sin mx and y = -sin (x/m) at the…

A: slope of the tangent at the point of taattngency = slope of the curve at the point of tangency =…

Q: A 5 kg weight is attached to a spring with constant k = 80 N/m and subjected to an external force…

A: Consider my¨+ky=Ft......1 Given that m=5 kg, k=80 Nm and Ft=140sin3t..…

Q: Find the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) =…

A: we are given the curve r(t)=3ti+e4tj+6e-tk we have to find the velocity vector , acceleration vector…

Q: A particle moves in a straight line with acceleration a(t) = sint + 3 cos t, initial displacement…

A: Given

Q: 2.x²y+ 3xy? = 2x + 55

A: We will find the value of dy/dx and the equation of the tangent line at point (5,1) in the following…

Q: EXAMPLE 1 (a) Find the derivative of r(t) = (4 + t4)i + te-tj + sin(2t)k. (b) Find the unit tangent…

A: Given data:     The given expression of the vector is: r(t)=(4+t4)i + te-tj +sin(2t)k.   (a) The…

Q: A mass oscillates up and down on the end of a spring. Find its position s relative to the…

A:

Q: The displacement from equilibrium of an oscillating mass attached to a spring is given by y(t) = 2…

A: The given equation for displacement from equilibrium of an oscillating mass attached to a spring is,

Q: b) Find the point's acceleration at the specified time. s"(2) = ft/sec2 %3D

A: we have been given  s=3t-3t2   , t=2s'(t)=ddt3t-3t2s'(t)=-3t2+6t3now…

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 direction in which the function g(x, y) = cos(xy) decreases fastest at the point (1, pi)

A:

Q: Find the speed (as a function of t ) of a particle whose position at time t seconds is c(t) = (sin t…

A:

Q: 3 E Eii %3D From the properties of characteristic equation of strain LEi 0 صواب ihi O

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A:

Q: A particle leaves the origin with its initial velocity given by v=23.8i - 143 m/s, undergoing…

A: Topic = Algebra

Q: The position of a vibrating spring after t seconds is given by f(t) = (1/2) cost − (1/5) sin t…

A: The given position of a vibrating spring is ft=12cost-15sint, where t is the time in seconds.…

Q: 2. A firefighter who weighs \(192\) lb slides down an infinitely long fire pole that exerts a…

A:

Q: u(x, y) = arctan a = (-1,0)

A:

Q: Use the tangent equation. tollowing equation to find the approximation at Co,0): fCX.y)e Jy+ cos cx)…

A: The given function is: f(x,y)=y+cos2x

Q: 12. Given the acceleration, Initial velocity, and initlal position of a body moving on a coordinate…

A:

Q: Find a parametric equation for the tangent line to the curve defined by r(t) = when t = 1.

A: Given is the equation of a 3-dimensional parametric equation, to find the equation of the tangent we…

Q: The parametric equations of a curve are given by x = In (Vi +1) and y = cosh (2t). dy Find the…

A: Use chain rule of differentiation to solve this problem.

Q: A sky diver weighing 192 lb (including equipment) falls vertically downward from a very high…

A: Given:

Q: Let C be the graph of the equation In(3y – 2e") = sinh (ma) - tan(y- 1). dy (a) Find da (b) Find an…

A:

Q: 1. If an object moves with velocity v(t) = sin(t) + 3t and begins at position p(0) = 0, find the…

A: integration of velocity funct

Q: In the figure particle 1 of charge +5e is above a floor by distance d1= 4.60 mm and particle 2 of…

A:

Q: Consider the step size h = 0.1 and h = 0.001, how does the step size affect the accuracy in %3D…

A: Given that, A=82, B=16.4f(x)=Aex+Bx2sinxFor the given values of A and B,f(x)=82ex+16.4x2sinxWe need…

Q: A 2 kg weight is attached to a spring with constant k = 8 kg/m and subjected to an external force =…

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…