frequency from steady state equation (simple) in Rad/s in Hertz Period Find the
ID: 2990057 • Letter: F
Question
frequency from steady state equation (simple)
in Rad/s
in Hertz
Period
Find the frequency, in radians/second, of the voltage source A sinusoidal source described by the function cos(omega t) has a frequency of radians/second. This means that the argument of the cosine function, omega t. has units of radians. The function cos(omega t) passes through a complete set of its values as omega t is varied from x radians to (x + 2pi) radians. Therefore, the frequency omega represents the rate at which the sinusoidal source oscillates. What is the frequency of the voltage source described as v(t) = 50cos(2000f - 45 degree) mV? Express your answer with the appropriate units. Enter your answer using dimensions of angular velocity. Find the frequency, in hertz, of the voltage source A sinusoidal source described by the function cos(omega t) has a frequency of omega radians/second. Using these units is often convenient but it may make visualizing the oscillating sinusoid more difficult. The units of hertz (abbreviated Hz) represents the number of cycles per second of oscillation and provides an easy way to picture the sinusoid. We often use the symbol f to represent the frequency in hertz, while we use the symbol u; to represent the frequency in radians/second. The relationship between f and u is given by the following equation: omega = 2pif What is the frequency of the voltage source described as v(t) = 50cos(2000t - 45 degree) mV? Express your answer to two digits after the decimal point and include the appropriate units. Find the period of the voltage source The period of a sinusoidal source is the time required for the sinusoid to pass through all of its possible values. We use the symbol T to represent the period of a sinusoid. The period and the frequency are inversely related. A sinusoidal source described by the function cos(omega t) has a frequency of omega radians/second, or a frequency f = omega /2piHz. The units hertz represents the number of cycles per second. Since the period is the number of seconds per cycle, the period is the inverse of the frequency in hertz: T = 1 / f Substituting the frequency in radians/second, omega . for the frequency in Hz gives us another way to calculate the period: T = 2pi / omega What is the period of the voltage source described as v(t) = 50 cos (2000t - 45 degree) mV? Express your answer to two digits after the decimal point and include the appropriate units.Explanation / Answer
1) 2000 rad/s
2)318.31 Hz
3)0.00314 s = 3.14ms
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