Acapacitor with plates separated by distance do is charged to a voltage difference δvc. all wires and batteries are disconnected, then the two plates are pushed together (with insulated handles so charges cannot flow) to a new separation distance that was half the original distance ( ). which of the following quantities will be doubled as a result of this new separation distance?
a. the capacitance of the capacitor, c.
b. the energy stored in the capacitor, u.
c. the magnitude of the electric field between the plates, ∣ e -> ∣.
d. the voltage drop across the capacitor, δvc
e. all of the above choices are correct.

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

For general projectile motion, when the projectile is at the highest point of its trajectory, its acceleration is zero? a)the horizontal and vertical components of its velocity are zero. b) its velocity is perpendicular to the acceleration. c)the horizontal component of its velocity is zero. d)its velocity and acceleration are both zero.

Imagine that someone pushes one marble toward a motionless marble. would there still be action-reaction forces involved in the collision? how might the marbles’ motions be changed? ?