Use an ideal op amp to design a differentiation circuit for which the time constant is 10‐3s usinga 10 nF capacitor. What are the gains and phase shifts found for the circuit at one‐tenth and 10times the unity‐gain frequency? A series input resistor is added to limit the gain magnitude athigh frequencies to 100 V/V. What is the associated 3‐dB frequency? What gain and phase shiftresult at 10 times the unity‐gain frequency?

Attached below is the detailed solution

Gains at one-tenth unity gain = 0.1 v/v

Gains at 10 times unity gain = 10 v/v

phase shift at 10 times unity gain =-95.71⁰

Explanation:

a)Gain at one-tenth unity gain

w/Wc = 100/1000 = 0.1 v/v

b)Gain at 10 times unity gain

w / Wc = 10 krad/sec / 1 krad/sec = 10 v/v

3-db frequency of new differentiator = 15.915 khz

attached below is the detailed solutions

prolly a beacuse the momentuem the car has increases while going down hill

an energy transformation flow diagram is shown

where is it ?