A support beam, within an industrial building, is subjected to vibrations along its length; emanating from two machines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelled by the following equations. x1 = 3.75 sin (100πt + 2?/9) ?2 = 4.42 sin (100?? − 2?/ 5) iii. At what time does each vibration first reach adisplacement of −2??? iv. Use the compound angle formulae to expand ?1and ?2 into the form ? sin 100?? ± ? cos 100??, where A and B are numbers to be found.

A support beam, within an industrial building, is subjected to vibrations along its length; emanating from two machines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelled by the following equations. x1 = 3.75 sin (100πt + 2?/9) ?2 = 4.42 sin (100?? − 2?/ 5) iii. At what time does each vibration first reach adisplacement of −2??? iv. Use the compound angle formulae to expand ?1and ?2 into the form ? sin 100?? ± ? cos 100??, where A and B are numbers to be found.

Name: A support beam, within an industrial building, is subjected to vibrati
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: A support beam, within an industrial building, is subjected to vibrations along its length; emanating from twomachines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelledby the following equations.x1 = 3.7

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter16: Oscillations

Section: Chapter Questions

Problem 28PQ: We do not need the analogy in Equation 16.30 to write expressions for the translational displacement...

See similar textbooks

Similar questions

We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.
The position 7 (in meters) of a particle of mass m (in kilograms) is described as two perpendicular oscillations that are out of phase with each other: 7 = rēi + yế2 = cos(wt)ěi + cos(wt + ø)ē2, where o is the constant phase angle difference. a. Show that the position 7 of the particle satisfies the harmonic oscillator equation -w?r. dt? Compute the particle's velocity v = dr/dt, dot product 7 · v, and angular momentum L = mĩ x v. Is the angular momentum constant in both magnitude and direction? b. Set w = 2 rad / s and ø = T/3 rad. Make a table with the following columns: t, x, y, Væ, Vy, and7· v. Put the units beside their respective variables and enclose the units inside the parentheses. Set the initial time to be to = 0 and use the spreadsheet to compute the values of xo, Yo, VOx, VOy, and ro · vo Write down the spreadsheet formula for the first xo, Yo, VOz, VOys and 7o - vo , assuming that the initial time to is spreadsheet cell A2.
Calendar A or B day Logic Games - Bra... Modeling with sinusoidal functions: phase shift A pendulum is swinging next to a wall. The distance from the bob of the swinging pendulum to the wall varies in a periodic way that can be modeled by a trigonometric function. The function has period 0.8 seconds, amplitude 6 cm, and midline H = 15 cm. At time t = 0.5 seconds, the bob is at its midline, moving towards the wall. Find the formula of the trigonometric function that models the distance H from the pendulum's bob to the wall after t seconds. Define the function using radians. H(t) = Report a problem Stuck? Watch a video or use a hint. Do 4 problems
TRIAL MASS ON PAN (M) TIME FOR 10 VIBRATIONS PERIOD, T T2 FREQUENCY, f 1 120 g 10 sec 2 150 g 15 sec 3 180 g 18 sec 4 210 g 18.75 sec 5 240 g 20 sec Complete the table.
An ultrasonic transducer that is used for medical diagnosis, oscillates with a frequency of 7.5 MHz. How much time does each oscillation take? O 133.3333 ns O 134.4333 ks O 134.4333 ns O 133.3333 ks
The human eardrum responds to sound by vibrating. If the eardrum moves in simple harmonic motion at a frequency of 2.88 kHz and an amplitude of 0.132 nm, what is its maximum speed of vibration? in. μm/s
A spring is hanging down from the ceiling, and an object of mass m is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up and down, and the time T required for one complete up-and-down oscillation is given by the equation T = 2л√m/k, wherek is known as the spring constant. What must be the dimension of k for this equation to be dimensionally correct? O [T] O [M] O [M]/[T] O [T]/[M] O [M]/[T]² O [T]²/[M]
The bob on a simple pendulum is pulled to the left 4 in. from its equilibrium position. After release, the pendulum makes one complete back-and-forth cycle in 2 sec and follows simple harmonic motion. a) Write a function to model the displacement d (in inches) of the bob as a function of time t (in seconds) after release. Assume that a displacement of the right of the equilibrium position is positive. b) Find the position and direction of movement of the bob at t=1.25 sec.
Period of a pendulum A standard pendulum of length L that swings under the influence of gravity alone (no resistance) has a period of T = 4 (/2 dọ w Jo Vi- k sin²o where o = g/L, k? = sin² (8,/2), g = 9.8 m/s² is the acceleration due to gravity, and 0, is the initial angle from which the pendulum is released (in radians). Use numerical integration to approximate the period of a pendulum with L = 1 m that is released from an angle of 0, = 7/4 rad. %3D
Q1:: The motion of particle by Parameter 54 X= sine Cos Ø Y v sin sing こ find T
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.
A particle is oscillating, following the equation: x=4 cos 5t+ 6 sin 5t, where x is in meters and t is in seconds. e Determine a) the period of the oscillation in seconds, b) the amplitude in meters and the phase angle in degrees, and c) the maximum velocity and maximum acceleration of the particle, in m/s and m/s² respectively.