Poisson bracket: prove that for one dimensional harmonic oscillator, H=p^2/2m+kx^2/2: x p H = = = p² 2m + {x, H} {p, H} ん-2 k = р m -kx
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dimensional harmonic oscillator,
H=p^2/2m+kx^2/2:
H
p² k
2m
+
x =
{x, H}
p = {p, H}
ん-2
=
=
Xx
р
m
-kx"
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- Final Answer must be decimal or whole number only!!!Adapt the method of Example 6 to determine the amplitude, period, and phase shift for the given function. Graph the function over one period indicating the x- intercepts and the coordinates of the highest and lowest points on the graph. (a) y = 3 cos(7 - 2x) amplitude period phase shift y y 3- 3 3 3 5/7 Зя 4 4 4 4 4 2 o-3 y 4. 4 2 x-intercepts (х, у) - (smaller x-value) (х, у) - (larger x-value) highest points (x, y) = (smaller x-value) (x, y) = (larger x-value) lowest point (x, y) =The midpoint of a guitar string executes simple harmonic motion with motion following the form x(t) = A sin(wt + p). It has an angular frequency of w = 2.65 × 10³ s-¹ and an amplitude of A = 1.50 mm. Take the phase constant to be p = π/2.
- What quantity is represented by the slope of the line? Frequency f Inverse Amplitude 1/A Period T Inverse spring constant 1/k Spring constant kAlert 1 of 1: Juniors and Seniors: Spring Formals S... F6 MULTIPLE CHOICE Graph What is the amplitude? F7 = = cos(x - 2) B А A-1/10 C −1+ -|N 3 D 1 õõo ő ő ő o 0 of 6 Total Questions Answered ooo DELL F8 2 Lake/0/ F9 DISMISS on your own graph paper. с F10 F11 Attempt 1 of 2 All Changes Saved F12 Insert t D 31 K Home D 4:49 P Ok 4/26/20 (())) Continue EndA particle oscillates according to x = Acos(ωt + δ) Determine the phase constant δ if the particle starts from x0 = −A.
- A pair of hoop earrings is in the form of peace signs and each earring can be made to oscillate with simple harmonic motion about the point where the earring is attached to the hook that goes through the ear lope. The earrings are made of cylindrical silver wire having a density of 10.2 g/cm3 and a diameter of 0.15 cm. Each earring can be thought of as consisting of a ring that is 1.5 cm in diameter, a central vertical rod that is 1.2 cm in length and two diagonal rods, each 0.6cm in length as shown in the diagram above. The distance from the pivot point of the earring to the center of mass of each diagonal rod is 0.975 cm. Based on this information, determine the period of this physical pendulum.The midpoint of a guitar string demonstrates simple harmonic motion with motion following the form x(t) = A sin (wt +ϕ). It has an angular frequency of w = 2.65 x 103 s-1 and an amplitude of A=1.50 mm. The phase constant is ϕ= pi/2. What is the maximum magnitude of the acceleration of the string?Two 1.3 kg masses and three identical springs having a k value of 85 N/m are connected. What are the frequencies of the two longitudinal vibration modes? The two periods? f=1/2π √(k/m)