A light balloon filled with helium of density 0.180 kg/m3 is tied to a light string of length L = 3.00 m. The string is tied to the ground, forming an “inverted” simple pendulum (Fig. P13.71a). If the balloon is displaced slightly from equilibrium, as in Figure P13.71b, show that the motion is simple harmonic and determine the period of the motion. Take the density of air to be 1.29 kg/m3.FIGURE P13.71

A small mass m is attached to a string of length L to make a simple pendulum that swings with period T. Suppose the mass is cut in half, what might the new period of oscillation be? Α. 2T T В. С.Т D. V2T An alien on Pluto has the exact same pendulum. What is the period of oscillation of the alien's pendulum in terms of T, given that the acceleration due to gravity on Pluto is 1/16 of the acceleration due to gravity on Earth? TPluto

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Chapter 15, Problem 014 A simple harmonic oscillator consists of a block of mass 1.40 kg attached to a spring of spring constant 350 N/m. When t 0.700 s, the position and velocity of the block are x oscillations? What were the (b) position and (c) velocity of the block at t 0 s? 0.115 m and v = 3.600 m/s. (a) What is the amplitude of the (a) Number Units (b) Number Units (c) Number Units

Consider an ideal spring with spring constant k = 20 N/m. The spring is attached to an object of mass m = 2.0 kg that lies on a horizontal frictionless surface. The spring-mass system is compressed a distance xo = 50 cm from equilibrium and then released with an initial speed vo= 0 m/s toward the equilibrium position. x=0 equilibrium initial state a. What is the period of oscillation for this system? b. Starting at t = 0, how long will it take for the object to first return to the equilibrium position?

A string attached to an oscillator at one end forms 5 nodes (counting the two ends) and produces a frequency of ν = 4.5 kHz. The string is L = 1.05 m long and is under a tension of T = 185 N.   a. What is the linear density of the string, in kilograms per meter?

Chapter 15, Problem 092 A grandfather clock has a pendulum that consists of a thin brass disk of radius r = 16.99 cm and mass 0.8660 kg that is attached to a long thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk, as shown in the figure. If the pendulum is to have a period of 1.541 s for small oscillations at a place where g = 9.820 m/s2, what must be the rod length L? Rotation axis dy Number Units

A string has length 2.0 m, tension 60 N, and linear density 0.080 kg/m. The left end of the string is connected to a massless ring that slides on a frictionless pole, and the ring is attached to a spring of stiffness 150 N/m. The right end is attached to a massless ring that slides on a frictionless pole. The left end of the string is driven by a transverse force of amplitude 4.0 N and frequency 21 Hz. F(t) X = 0 x = L 1. Determine the distance (in m) between adjacent nodes of the steady-state standing wave produced by the force.