6. a particle of mass is released from the position a of a semi-sphere and moves frictionless on its inner surface as shown in the figure. i) plot the force - cos diagram. ii) calculate the magnitude of the velocity ⃗ of the particle at the position a so that the magnitude of the force exerted on the particle at the position c to be = 4. 7. two perpendicular planes one made up from wood and the other from plastic are in contact as shown in the figure. the depth of each plane is = 5 . the projectile a passes through the wooden plane and stops inside the plastic plane at a distance of 1= 2 . the projectile c passes through the plastic plane and stops inside the wooden one at a distance of 2 = 1 . if the resistance forces on the projectiles from the wood and plastic are assumed constant during the motion of the projectiles, calculate the ratio ⁄.

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

Critical mass is the of material required to produce a chain reaction. a.) minimum amount b.) atomic mass c.) precise amount d.) maximum amount

Can you match these to the correct definition