FIGURE EX15.7 is the position-versus-time graph of a particle in simple harmonic motion.a. What is the phase constant?

At a distance of 7.00x10^12 m from a star, the intensity of the radiation from the star is 15.4 W/m^2. Assuming that the star radiates uniformly in all directions, what is the total power output of the star?

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x, t)=2.30mm cos[(16.98 rad/m^)x+(742 rad/s)t]. Being more practical, you measure the rope to have a length of 1.35 m and a mass of 0.00338 kg. You are then asked to determine the following: (f) tension in the rope; (g) average power transmitted by the wave.

Suppose a large spherical object, such as a planet, with radius R and mass M has a narrow tunnel passing diametrically through it. A particle of mass m is inside the tunnel at a distance 𝓍 ≤ R from the center. It can be shown that the net gravitational force on the particle is due entirely to the sphere of mass with radius 𝓇 ≤ 𝓍 there is no net gravitational force from the mass in the spherical shell with 𝓇 > 𝓍.a. Find an expression for the gravitational force on the particle, assuming the object has uniform density. Your expression will be in terms of x, R, m, M, and any necessary constants.

What are the (a) amplitude, (b) frequency, and (c) phase constant of the oscillation shown in FIGURE EX15.6?

An object in SHM oscillates with a period of 4.0 s and an amplitude of 10 cm. How long does the object take to move from x = 0.0 cm to x = 6.0 cm?

FIGURE EX15.7 is the position-versus-time graph of a particle in simple harmonic motion.c. What is vₘₐₓ?

The amplitude of an oscillator decreases to 36.8% of its initial value in 10.0 s. What is the value of the time constant?

An object in simple harmonic motion has an amplitude of 8.0 cm, n angular frequency of 0.25 rad/s, and a phase constant of π rad. Draw a velocity graph showing two cycles of the motion.