Problem 3: Obtain time-domain mathematical model of the following circuit.

An accelerometer is used to detect ultra-low-level, low-frequency vibrations (100 Hz)associated with very large structures. It possesses a natural frequency of 1000 Hz witha damping ratio of 0.05 and sensitivity of 2V/g. Write down the order of the systemand its differential equation

You are asked to build a sinusoidal waveform generator for a frequency of 10,000 Hz. You have not designed this before. You start a brainstorming session with your team by examining a series RLC circuit. One of your team members points out that the step response of the series RLC circuit with complex roots would have an exponentially decaying sinusoidal response. The team member argues that if we eliminate exponent from the time response by making appropriate changes in the circuit or component values, we could get a sinusoidal signal at any desired frequency. After some discussion you decide to follow this approach. 1. Design a series RLC circuit with a resonant frequency of 10 kHz. Use C = 1.0 nF and compute the other component values for your design. 2. Implement and test the circuit. Document all your measurements and observations. Questions: 1. Were you able to design, build, and test the circuit to meet all the requirements of this experiment? Please explain any discrepancies in…

C.topic is all about APPLICATIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONSplease show complete solution3. Find the charge on the capacitor and the current in the given RLC series circuit whose values aregiven below. Find the maximum charge of the capacitor.L = 1H                    E(t) = 30VC = 0.0004F           q(0) = 0CR = 100Ω                i(0) = 2A

Write the differential equation that is mathematically equivalent to the block diagram shown in the figure below. R(s) C(s) s4 + 3s3 + 2s2 + s + 1 55 + 4s4 + 3s3 + 2s2 + 3s + 2