What is the total distance traveled by an object moving back and forth in simple harmonic motion in a time interval equal to its period when its amplitude is equal to A?

A wave is modeled by the wave function y(x, t) = (0.30 m)sin[(2π/4.50 m)(x - 18.00(m/s)t)]. What are the amplitude, wavelength, wave speed, period, and frequency of the wave?

It has been discovered that an exhaust fan with an operating speed of 1000 rpm and a mass of 80 kg exerts a repeated force of 10,000 N on its rigid base. Determine (a) the maximum permissible stiffness of the isolator that serves the purpose, (b) the steady-state amplitude of the exhaust fan with the isolator that has the maximum permissible stiffness, and ( c ) the maximum amplitude of the exhaust fan with isolation during start-up if the maximum force transmitted to the base is to be limited to 2000 N.

A trigonometric function is given. (a) Find the amplitude, period, and horizontal shift of the function. (b) Sketch the graph.

$$y = - \cos \left( \frac { \pi } { 2 } x + \frac { \pi } { 6 } \right)$$

Explain why Kent is correct.

Kent: -

The equation $b(t)=|A| \cdot 0.9^ t$ describes the change in the object's height over time, because |A| represents the amplitude of the function.

Determine the theoretical probability of the outcome.

The probability of tossing two coins and having them land heads up is $\frac{1}{4}$. What is the probability the coins will not land heads up?

A mass moves back and forth in simple harmonic motion with an amplitude of 0.25 m and a period of 1.2 s. Through what distance does the mass move in 2.4 s?

Write expressions for the electric and magnetic fields of a sinusoidal plane electromagnetic wave having an electric field amplitude of 300 V/m and a frequency of 3.00 GHz and traveling in the positive x direction.

Determine the number of cycles each sine function has in the interval from 0 to $2 \pi.$ Find the amplitude and period of each function. $y=3 \sin \theta$

Choose the word or phrase that best answers the question. Which property of a wave increases when its frequency decreases? A. amplitude, B. crest, C. speed, D. wavelength.

Refer to the previous exercise. The carbon dioxide content in the atmosphere at Barrow, Alaska, in parts per million (ppm) can be modeled using the function defined by

$$C(x)=.04 x^2+.6 x+330+7.5 \sin (2 \pi x),$$

where $x=0$ corresponds to $1970$.

Discuss possible reasons why the amplitude of the oscillations in the graph of $C$ is larger than the amplitude of the oscillations in the graph of $L$ in the previous exercise, which models Hawaii.

What is the total distance traveled by an object moving back and forth in simple harmonic motion in a time interval equal to its period when its amplitude is equal to A?

A trigonometric function is given. Find the amplitude, period, phase, and horizontal shift of the function. $y=2 \sin \left(\frac{1}{2} x-\frac{\pi}{6}\right)$

Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for

$$0 \leq x \leq 2 \pi.$$

$$y = \frac { 1 } { 3 } \sin x$$