2 Questions
Question 1:
Two vibrations, x1 = 3sin (10t + pi/6) and x2 = 2 cos (10t - pi/6) where t is in seconds, are superimposed. Determine the time at which the amplitude of the resultant vibration, x1 + x2, first reaches a value of 2.
Question 2:
The instantaneous current and voltage in an electric circuit are given by
i = I cos 50pi t
v = Vcos (50 pi t + pi/6)
determine an expression for the instantaneous power in the circuit, p = iv, as the sum of two cosines.
If I is 3mA and V is 5 V, calculate the maximum value of p, giving your answer in watts correct to three significant figures, and the first positive value of t at which it occurs.
The solution is comprised of detailed explanations of superimposition of two vibrations and the resultant vibration. It also explains the calculation of instantaneous power in the circuit.
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