Q) A pendulum with a bob of 100 g is initially displaced from its equilibrium position and released from a height of 60 cm above the equilibrium. Upon release, it undergoes simple harmonic motion (SHM) without any energy losses to its surroundings. a) What is the type of energy the pendulum possesses at the point of release?
b) Calculate the amount of this type of energy at the point of release.
c) What happens to this type of energy as the bob starts moving towards its equilibrium position?
d) What is the type of energy the pendulum possesses at its equilibrium position?
e) Calculate the maximum speed of the bob of the pendulum as it swings back and forth in SHM.
f) Suppose we were to design a harmonic oscillator with a mass of 100 g to move with the same maximum speed as the pendulum. What would the stiffness of the spring need to be if we assume the harmonic oscillator to have a maximum horizontal displacement of that is half of the initial vertical displacement of the pendulum?

Some material consisting of a collection of microscopic objects is kept at a high temperature. a photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of 0.3 ev, 0.5 ev, 0.8 ev, 2.0ev, 2.5ev, and 2.8ev. these are the only photon energies observed. (a) draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. on the diagram, indicate the transitions corresponding to the emitted photons. explain briefly. (b) would a spring–mass model be a good model for these microscopic objects? why or why not? (c) the material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. what photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? explain briefly.