An object of mass 0.03 kg is displaced from its equilibrium position at x = 0 to a distance x = 40 cm and is then released. The restoring force acting on the object is proportional to its displacement and acts in the opposite direction of the displacement. The period of an oscillating particle is 2.0 sec. Write equations for (a) the position x versus t,

An object of mass 0.03 kg is displaced from its equilibrium position at x = 0 to a distance x = 40 cm and is then released. The restoring force acting on the object is proportional to its displacement and acts in the opposite direction of the displacement. The period of an oscillating particle is 2.0 sec. Write equations for (a) the position x versus t, (b) the velocity v versus t, (c) the acceleration a versus t, and find (d) the maximum velocity of the particle, (e) the maximum acceleration of the particle and (f) its total energy.
A simple pendulum 2.50 m long swings with a maximum angular displacement of 16°. Find its (a) period of vibrations, (b) frequency of vibrations, (c) linear speed at its lowest point of vibration, and (d) linear acceleration at the end of its path.
A spherical ornament of mass 0.01 kg and radius 0.20 m is doing simple harmonic motion about an axis passing through its surface. It swings back and forth as a physical pendulum. Find its period of oscillation.
A 0.540 kg mass is attached to the end of a spring with force constant k = 300 N/m. The object is displaced and released. A damping force F = −b v acts on the object where b = 7.5 kg/s. (a) Find the frequency of the oscillation of the mass. (b) For what value of b will the motion be critically damped?
The motion of a particle connected to a spring is described by x = 10 sin (πt). At what time (in s) is the potential energy equal to the kinetic energy?
An archer pulls her bow string back 0.40 m by exerting a force that increases uniformly from zero to 240 N. What is the equivalent spring constant of the bow, and how much work is done in pulling the bow?
For the wave described by , determine the first positive x coordinate where y is a maximum when t = 0.
Answer the following questions in as much detail as possible. Once you have completed your post, respond to the post of at least 2 of your classmates. 1. Nikola Tesla, one of the inventors of radio and an archetypal mad scientist, told a credulous reporter in 1912 the following story about an application of resonance. He built an electric vibrator that fit in his pocket, and attached it to one of the steel beams of a building that was under construction in New York. Although the article in which he was quoted didn’t say so, he presumably claimed to have tuned it to the resonant frequency of the building. “In a few minutes, I could feel the beam trembling. Gradually the trembling increased in intensity and extended throughout the whole great mass of steel. Finally, the structure began to creak and weave, and the steelworkers came to the ground panic-stricken, believing that there had been an earthquake. … [If] I had kept on ten minutes more, I could have laid that building flat in the street.” Is this physically plausible? 2. A sound wave that underwent a pressure-inverting reflection would have its compressions converted to expansions and vice versa. How would its energy and frequency compare with those of the original sound? Would it sound any different? What happens if you swap the two wires where they connect to a stereo speaker, resulting in waves that vibrate in the opposite way?