Find amplitude from a sinusoid equation

Question

I want to find the Amplitude, frequency, time period and phase from this equation. I know how to find the frequency, time period or phase shift but I'm confused if there's any way to find the amplitude from the given information. A/5 *in (1000 + 120)

Answer 1

Since the equation is of the form f(t) = (A/5)*sin(ϕ) where ϕ is called the phase and is of the form "100t + 120" in this case. Since you said that you know how to find the phase, frequency and the time-period, I shall not be getting into that.

Since f(t) is a function of time (assuming a constant A with respect to t), and the maximum absolute value of a sinusoidal is always 1 i.e. max{|sin(ϕ)|} = 1 which means the sinusoidal oscillates between +1 and -1, so the value of f(t) oscillates between +A/5 and -A/5.

The amplitude of a wave is nothing but the difference between the peaks and the troughs, which, in this case, is +A/5 - (-A/5) which is 2A/5.

Hence, the amplitude of the given wave is 2A/5.