Determine the initial displacement, velocity and acceleration of the midpoint of the string. 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.

Determine the initial displacement, velocity and acceleration of the midpoint of the string. 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.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter13: Continuous Systems; Waves

Section: Chapter Questions

Problem 13.9P

See similar textbooks

Similar questions

The expression x = 8.50 cos (2.40 t + /2) describes the position of an object as a function of time, with x in centimeters and t in seconds. What are the a. frequency, b. period, c. amplitude, and d. initial phase of the objects motion? e. What is the position of the particle at t = 1.45 s?
A suspension bridge oscillates with an effective force constant of 1.00108 N/m . (a) How much energy is needed to make it oscillate with an amplitude of 0.100 m? (b) If soldiers march across the bridge with a cadence equal to the bridge’s natural frequency and impart 1.00104 J of energy each second, how long does it take for the bridge’s oscillations to go from 0.100 m to 0.500 m amplitude.
A spherical bob of mass m and radius R is suspended from a fixed point by a rigid rod of negligible mass whose length from the point of support to the center of the bob is L (Fig. P16.75). Find the period of small oscillation. N The frequency of a physical pendulum comprising a nonuniform rod of mass 1.25 kg pivoted at one end is observed to be 0.667 Hz. The center of mass of the rod is 40.0 cm below the pivot point. What is the rotational inertia of the pendulum around its pivot point?
Suppose you have a 0.750-kg object on a horizontal surface connected to a spring that has a force constant of 150 N/m. There is simple friction between the object and surface with a static coefficient of friction s=0.100 . (a) How far can the spring be stretched without moving the mass? (b) If the object is set into oscillation with an amplitude twice the distance found in part (a), and the kinetic coefficient of friction is k=0.0850 , what total distance does it travel before stopping? Assume it starts at the maximum amplitude.
An automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for every additional 100 kg of passengers. It is driven with a constant horizontal component of speed 20 km/h over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 5.0 cm and 20 cm, respectively. The distance between the front and back wheels is 2.4 m. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.
Need help with part A and B and C pls. Part C asks: If the angular displacement can be written as θ=Ae^(−γt)cosω′t, find how long it takes for the amplitude to be reduced to 1/2 of its original value.
For y = 10 cos(x) + 5, %3D the midline is y = the amplitude is
A uniform disk of radius 4.7 m and mass 8.7 kg is suspended from a pivot 3.102 m above its center of mass. The acceleration of gravity is 9.8 m/s². axis Find the angular frequency w for small os- cillations. Answer in units of rad/s.
An M = 12.3 kg mass is suspended on a k = 273000 N/m spring. The mass oscillates up-and-down from the equilibrium position Yeq = 0 according to y(t) = A sin(wt + $0). Calculate the angular frequency w of the oscillating mass. Answer in units of s-¹. S At time to = 0 the mass happens to be at yo = 19.8 cm and moving upward at velocity vo +58.4 m/s. (Mind the units!) Calculate the amplitude A of the oscillating mass. Answer in units of cm. CHOOSE Calculate the initial phase do. Answer in range 0 0 < 360°. Answer in units of ᵒ. Calculate the position of the oscillating mass at the time t = 0.0662 s. Answer in units of cm.
Two parallel S.H.M.s are given by x₁ = π 20 sin 8 t and x² = 10 sin (8π t +). Find the (8T initial phase of resultant amplitude and resultant S.H.M.
The differential d²x dt² S.H.M. is given by — equation for linear 4x. If the amplitude T is 0.5 m and initial phase is radian, obtain the displacement equation of S.H.M. and find the velocity at x = 0.3 m for the particle in S.H.M.
s An atom in a molecule oscillates about its equilibrium position with a frequencyof 2.00 * 1014Hz and a maximum displacement of 3.50 nm.(a) Write an expression giving x as a function of time for this atom,assuming that x = A at t = 0. (b) If, instead, we assume that x = 0at t = 0, would your expression for position versus time use a sinefunction or a cosine function? Explain.