Consider a system of three harmonic oscillators (SHOs), each with possible energies 0, 1ε, 2ε, 3ε, ... If you are given the total energy, then you know that the sum of all the oscillators' energies is equal to the total energy. One way to compute how many microstates there are is to write down how many states there are if the first oscillator has 0, 1, 2, and 3 ϵ energy, then sum them all together.

Suppose a force of 60 n is required to stretch and hold a spring 0.1 m from its equilibrium position. a. assuming the spring obeys hooke's law, find the spring constant k. b. how much work is required to compress the spring 0.5 m from its equilibrium position? c. how much work is required to stretch the spring 0.6 m from its equilibrium position? d. how much additional work is required to stretch the spring 0.1 m if it has already been stretched 0.1 m from its equilibrium? a. kequals 600