Write the equation of a sinusoidal function that has a minimum at (-4, 1) and a maximum at (1, 11). Sketch two complete periods of your equation.
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- A sinusoidal function has a minimum point at (2,4) it has an amplitude of 3. Use this to determine the equation of the midline and the value of the maximum. Explain with use of a sketchCoupled Harmonic Oscillators X2 :0 eeeee Leeee NM ) Write down the 2nd law for each of the masses. Use coordinates x, aud x, for m and M, and i,, *2 and a, a2. Hirnt: the force from spring I on monly depends on x, , but the ferce from spring 2 on m depand s on (x2-x,) two differantial 2) To simplify, let k, -k,k and m-M. Rewrite egg equatious from i) right above each other. your 3) Detine two new variables, X (Greek"chi") - x,+X2 and Ax = X,-x 2 two di ferential equations to produce Then add and subtract your very simple (harmanic) ones. 4) Write down the solutiou to bothe equations using Wask+2k2 ond evefficients A, B, C, and D two new , but w. : un 5) Now assune k-10k2 (this means that the two masses are "weakly coupled"). Also assume X,(0) = -10cm, x,(0)=0, xz (0)= o, x,(0)=0. Solve for A,B, C, D, and solve for x (t).Graph the functions. Then find the extreme valuesof the function on the interval and say where they occur. h(x) = |x + 2| - |x - 3 |, -∞ < x <∞
- By using hamiltonian equations. Find the solution of harmonic oscillator in : A-2 Dimensions B-3 dimensionsPlease answer in detail and I will upvote. Thank you.Consider a mass m attached to a spring with natural length 7, hanging vertically under the action of gravity mgk (where the unit vector k is pointing downwards) and a constant friction force F =-Fok. (a) Find the equilibrium point of the mass, write the equation of motion, and show that the motion of the particle is governed by the fundamental equation of simple harmonic motion. (b) Assume the particle is released from the spring when it has heighth above ground and initial velocity vo. Let y be the height above ground of the particle (note that the orientation of the axis is now opposite of z used in point (a)). Write the equation of motion (under the action of gravity and the friction force F). Solve them for the given initial condition and show that v(y)² = vz+2(g− ¹)(h—−y) m (c) Upon entering the ground (y=0) with velocity v₁, the particle is subject to a constant friction force F₁ where F₁ >0 is a constant. Calculate the distance d travelled by the particle into the ground in…
- Two pendulums have equal length L, but different masses mị and m2. The pen- dulums are coupled by a spring with spring constant K. The pendulums can only move in the plane of the figure. Find the frequencies of small oscillations around the equilibrium point. Use arrows on a picture like the one below to show the ap- proximate displacements corresponding to these modes. You do not need to find algebraic expressions for the displacements. Escape clause: if this problem is a little too hard, you will get partial credit for solving the special case mı = m2. L |L ml m2 kPlease, I want to solve the question correctly, clearly and conciselySuppose that you have a potential V (x) x2 + 6x – 8. Using a Taylor Series around Xo = 3, approximate the potential as a harmonic oscillator. O + (= – 3)? 7-2 (포-3)2 | (x – 3)? ||