My question is, how do you know when to use cos or sin?? Please be as specific as possible, thank you! "An object is attached to a coiled spring. The object begins at its rest position at t=0 seconds. It is then propelled downard. Write an equation for the distance of the object from its rest position after t seconds, if the amplitude

My question is, how do you know when to use cos or sin?? Please be as specific as possible, thank you! "An object is attached to a coiled spring. The object begins at its rest position at t=0 seconds. It is then propelled downard. Write an equation for the distance of the object from its rest position after t seconds, if the amplitude

Name: Below I have 2 very similar equations that both use cos and sin within
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Description: Below I have 2 very similar equations that both use cos and sin within their answers.My question is, how do you know when to use cos or sin?? Please be as specific as possible, thank you! "An object is attached to a coiled spring. The object begins a

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 55PQ

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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?
Below I have 2 very similar equations that both use cos and sin within their answers. My question is, how do you know when to use cos or sin?? "An object is attached to a coiled spring. The object begins at its rest position at t=0 seconds. It is then propelled downard. Write an equation for the distance of the object from its rest position after t seconds, if the amplitude is 5 inches and the period is 4.5" d= -5sin(4pi t /9) "An object is attached to a coiled spring. The object begins at its rest position at t=0 seconds. It is then propelled downard. Write an equation for the distance of the object from its rest position after t seconds, if the amplitude is 9 inches and the period is 4.5" d= -9cos(4pi t/9)
I simplified the problem A simple pendulum consists of a bob of mass of 0.85 kg attached to a string of length 1.5 m. The pendulum is raised to point Q, which is 0.08 m above its lowest position, and released so that it oscillates with a small amplitude θ between the points P and Q as shown below. 1. Calculate the total energy of the oscillating system. 2. Determine the height at which the potential and kinetic energies are equal.
An oscillator moves back and forth between the 10 cm and 50 cm marks on a meter stick. What is the location of the EP on the meter stick? In Problem 11, what is the amplitude A?
1. Sinewave A lags sinewave B by 30°. Both have peak values of 15V. Sinewave A is the reference with a positive going crossing at 0º. Determine the instantaneous value of sinewave B at 30°, 45°, and 2000. 2. Make a sketch of two sinewaves as follows. Sinewave A is the reference and sinewave B lags A by 90°. Both have equal amplitudes.
The phase space trajectory of an undamped oscillator is shown below. In the diagram, eachdivision along the position axis corresponds to 0.1 m; along the velocity axis, 0.10 m/s. What is the angular frequency ?Aof the undamped oscillator? Explain how you can tell.
The motion of a mass and spring is described by the following equation: 11y"+4y+6y= 35 cos(yt) Identify the value of y that would produce resonance in the system. Give an exact value, but you don't need to simplify radicals. Y What is the amplitude of the steady-state solution when the system is at resonance? Round your answer to two decimal places. The amplitude is If there was no external force, the oscillation of the spring could be described in the form A sin(ßt + p). What is the value of B? Give an exact value, but you don't need to simplify radicals. В
The figure below shows a piston from your car engine. Don't worry, you will not be required to understand an internal combustion engine for this problem. Instead, we simply notice that the up/down motion of the piston is exactly described as Simple Harmonic Motion. The tachometer on your dashboard tells you that your engine is turning at w = 1660 rpm (revolutions/minute). The owner's manual for your car tells you that the amplitude of the motion of the piston is Ymax = A = 0.099 meters. Simple Harmonic Motion wrist pin 500 grams Crankshaft A (top of stroke) B (midpoint) -C (bottom of stroke) y=-A y=+A Determine all the following: The angular frequency in proper units w = The period of the piston, T = The frequency of the piston, f = The maximum velocity of the piston, Vmax = meters/sec The piston velocity when y = 58% of full stroke, v(y = 0.58 Ymax) = seconds Hz rad/sec meters/sec
revolves U diameter ground A Ferris wheel is 28 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 16 minutes. The function h (t) gives a person's height in meters above the ground t minutes after the wheel begins to turn. a. Find the amplitude, midline, and period of h (t). Enter the exact answers. Amplitude: A = Number meters Midline: h= Number meters Period: P = Number minutes b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t = 0. Find a formula for the height function h (t). Hints: • What is the value of h (0)? • Is this the maximum value of h (t), the minimum value of h (t), or a value between the two? • The function sin (t) has a value between its maximum and minimum at t = 0, so can h (t) be a straight sine function? • The function cos (t) has its…
There are three identical rods and each of the has a mass of 1 kg and length of 39.2 cm. They are used in constructing a rigid body as seen in the figure. What is the period of small oscillations if it was pivoted at an axis through P? Take note that the center of mass of the rigid body is at Q. L L You can choose your answer here: 1.26 s 0.51 s 0.85 s 0.20 s L/2 P Q L/2
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Part D) For a cosine function with amplitude A=0.75�=0.75 and period T=10�=10, what is y(4)�(4)? Express your answer to three significant figures.