Using the equipartition theorem calculate the heat capacities Cv and Cp for N systems of: a) Free particles b)
1-dimensional harmonic oscillators. c)
3-dimensional harmonic oscillators.
d) Monoatomic, diatomic and triatomic molecules.
e) Molecules having 3f degrees of freedom. ​

Will a heavier bowling ball hit pins better than a lighter bsll

Fft review: linspace, fs, fftshift, nfft 1. generate one second of a cosine of w,-10hz sampled at f, = 100hz and assign it to x. define a tt as your time axis 2. take 64 points fft. 3. as you remember, the dft (which the fft implements) computes n samples of s2t where k-0,1,2, n -1. plot the magnitude of this 64-points fft at range 0 to 63, what do you think of this graph? 4â·to get the x-axis into a hz-frequency form, plot this 64-points fft between-50 to 50 (the 100hz sampling rate) and have n-points between them. 5. according to your figure, what frequency is this cosine wave at? 6. remember that the fft is evaluating from 0 to 2ď€. we are used to viewing graphs from-ď€ to ď€. therefore, you need to shift your graph. 7. now according to your shifted graph. what frequency is this at? 8. note that the spikes have long drop-offs? try a 1024-point dft. note that the peak is closer to 10 and the drop-off is quicker. although, now sidelobes are an issue

Given the position vector of the particle r(t)=(t+1)i+(t^2−1)j+2t k, find the particle's velocity and acceleration vectors at t=1