An object in simple harmonic motion has an amplitude of 8.0 cm, a frequency of 0.25 Hz, and a phase constant of $-\pi/2$ rad. Draw a position graph showing two cycles of the motion.

Use a graphing calculator to determine whether the equation could be an identity by graphing each side of the equation on the same screen. Then prove or disprove the statement algebraically. $\frac { \sin 2 x } { 2 } = \sin x$

The public library has a mural that measures 15 meters wide. Select all the customary measures that are greater than 15 meters.

$\boxed{ \text{ }}$500 in.$\boxed{ \text{ }}$550 in.$\boxed{ \text{ }}$600 in.$\boxed{ \text{ }}$45 ft$\boxed{ \text{ }}$50 ft

An object in simple harmonic motion has an amplitude of 4.0 cm, a frequency of 2.0 Hz, and a phase constant of $2\pi/3$ rad. Draw a position graph showing two cycles of the motion.

When a guitar string plays the note "A," the string vibrates at 440 Hz. What is the period of the vibration?

What are the (a) amplitude, (b) frequency, and (c) phase constant of the oscillation

In a completely inelastic collision between two objects, where the objects stick together after the collision, is it possible for the final kinetic energy of the system to be zero? If so, give an example in which this would occur. If the final kinetic energy is zero, what must the initial momentum of the system be? Is the initial kinetic energy of the system zero? Explain.

A block oscillating on a spring has a maximum speed of 20 cm/s. What will the block's maximum speed be if the total energy is doubled? Explain.

Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients. x^4 - 2x^3 + x^2 + 2x - 1 / x^2 - 2x + 1

Consider the liquid in a barometer whose coefficient of volume expansion is

$$6.6\times10^{-4}/{C^\circ}$$

. Find the relative change in the liquid’s height if the temperature changes by

$${12\ C^\circ}$$

while the pressure remains constant. Neglect the expansion of the glass tube.

Graph the system of inequalities.

$$\left. \begin{array} { l } { y < - 2 x + 3 } \\ { y \geq 4 } \end{array} \right.$$

An object is oscillating in simple harmonic motion with an amplitude A and an angular frequency $\omega$. What should you do to increase the maximum speed of the motion? (a) Reduce both A and $\omega$ by $10 \%$. (b) Increase A by $10 \%$ and reduce $\omega$ by $10 \%$. (c) Reduce A by $10 \%$ and increase $\omega$ by $10 \%$. (d) Increase both A and $\omega$ by $10 \%$.

An air-track glider attached to a spring oscillates between the 10 cm mark and the 60 cm mark on the track. The glider completes 10 oscillations in 33 s. What are the (a) period, (b) frequency, (c) angular frequency, (d) amplitude, and (e) maximum speed of the glider?

The position of a 50 g oscillating mass is given by x(t) = (2.0 cm) cos (10 t), where t is in seconds. Determine: a. The amplitude. b. The period c. The spring constant d. The maximum speed. e. The total energy. f. The velocity at t = 0.40 s.