following set of linear differential equations: 0.02 w+ 0.15w = 0.03i, 0.7 di/dt + 3i = v - 0.03w. where w(t) is the rotational speed in rad/s, i(t) is the current in Amperes, and v(t) is the input voltage in Volts. Calculate the transfer function P(s) = w(s) V (s) assuming zero initial conditions. What is the (a) damping ratio 7 and (b) natural frequency wn of the DC motor?

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B4
A certain DC motor is governed by the
following set of linear differential equations:
0.02 w+ 0.15w = 0.03i,
0.7 di/dt + 3i = v - 0.03w.
where w(t) is the rotational speed in rad/s,
i(t) is the current in Amperes, and v(t) is the
input voltage in Volts. Calculate the transfer
function P(s) = w(s) V (s) assuming zero
initial conditions. What is the (a) damping
ratio and (b) natural frequency wn of the
DC motor?
Transcribed Image Text:A certain DC motor is governed by the following set of linear differential equations: 0.02 w+ 0.15w = 0.03i, 0.7 di/dt + 3i = v - 0.03w. where w(t) is the rotational speed in rad/s, i(t) is the current in Amperes, and v(t) is the input voltage in Volts. Calculate the transfer function P(s) = w(s) V (s) assuming zero initial conditions. What is the (a) damping ratio and (b) natural frequency wn of the DC motor?
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