There are three questions each task need to be solved step by step with full calculation and explanation as well as drawings and sketches where required.

Q1. Explain when a sinusoidal electrical waveform conducted through a pn junction diode to a resistive load, does not appear sinusoidal across the resistor. Draw a circuit diagram and also show the waveforms from source and across the load.

Q2. A complex voltage waveform is composed of harmonics and is described by the following expression:

v = 200 sing(ωt + π/6) + 150 sin (2ωt - π/3) + 75sin(3ωt + π/5) V

is applied to the following circuits comprising of pure components of:

i) 25 Ω resistor,

ii) 25x10^-3 H inductor,

iii) 25x10^-6 F capacitor.

The fundamental frequency is 500 Hz. Determine the current expression flowing in each separate circuit.

In the DC circuit shown above, apply Thevenin's Theorem to find the current in the 25Ω resistor.

Q3. Energy transfer in mechanical systems-

a. A spring is initially compressed by 50mm when a steel ball of mass 2 Kg is released from just being in contact with the uncompressed spring. Determine

i. The spring stiffness (k) of the spring

ii. The amount the spring would be compressed if the mass is dropped from 200mm above the spring.