Consider a classical simple harmonic oscillator (as defined in the readings') that consists of a fric- tionless particle of mass of m kilograms bound by a conservative restoring force with a magnitude of k newtons per meter of displacement from equilibrium. consider the case in which the particle is initially at rest but displaced from equilibrium by x1 meters and released at time t =0 seconds. clearly, the results must be presented symbolically in terms of the given values a what is the period of oscillation, т, in seconds, of the particle? b what is the marimum kinetic energy that the particle achieves, in j? at what position(s) does it achieve this kinetic energy? at what time(s) after release does the particle achieve marimum kinetic energys c what is the time-averaged potential energy of the particle? at what position(s) does it achieve this potencial energy? at what time(s) after release does the particle achieve this potential energy? d sketch the particle's position, momentum, potential energy, and kinetic energy as a function of time e sketch the spatial probability distribution of the particle, i. e., the function that describes where one is most likely to find the particle at an arbitrary time

Determine the amount of work done when a crane lifts a 100-n block form 2m above the ground to 6m above the ground

State one advantage and one disadvantage of using a plane mirrior as a driving mirrior

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.