Asimple harmonic oscillator consists of a block (m = 0.50 kg) attached to a spring (k = 128 n/m). the block is pulled a certain distance from the equilibrium position and released at t = 0 s. the block slides on a horizontal frictionless surface about the equilibrium point x = 0 m with a total mechanical energy of 16 j. a) what are the amplitude and phase constant of the oscillation? b) find the period of the motion and determine the number of oscillations (cycles) the block completes during a 5.5 s interval? c) find the maximum speed the block will achieve and the time at which it first occurs. d) find the speed of the block at the instant it is displaced 0.35 m from its equilibrium position.

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

Acup of coffee sits on the dashboard of an automobile. the car goes around a sharp curve. even though you hold the cup still, coffee still splashes out. this can best be explained due to a) density. b) friction. c) gravity. d) inertia.

The arrival of in the early days of europa’s existence could have formed its ocean. it is likely that the water experienced similar to earth. it is also possible that this water is retained beneath europa’s surface and in its atmosphere due to europa’s . 1.) a. precipitation b. water vapor c. icy debris 2.) a. gravitational compression b. biochemical cycling c. radiogenic heating 3.) a, gravity b. magnetic field c. heat energy for plato