Question

Find a function that models the simple harmonic motion given amplitude period.

a) f(x) = A * sin(2π/T * x)
b) f(x) = A * cos(2π/T * x)
c) f(x) = A * sin(T * x)
d) f(x) = A * cos(T * x)

Answer 1

The functions modeling simple harmonic motion with given amplitude A and period T are f(x) = A * sin(2\u03c0/T * x) and f(x) = A * cos(2\u03c0/T * x), which correspond to options (a) and (b) respectively.

Step-by-step explanation:

To find a function that models simple harmonic motion given amplitude (A) and period (T), we should remember the basic form of a simple harmonic motion equation is x(t) = A cos (\(2\pi f t + \phi\)) or x(t) = A sin (\(2\pi f t + \phi\)), where A is the amplitude, f is the frequency, and \(\phi\) is the phase shift.

The functions modeling simple harmonic motion with given amplitude A and period T are f(x) = A * sin(2\u03c0/T * x) and f(x) = A * cos(2\u03c0/T * x), which correspond to options (a) and (b) respectively. The frequency f is the reciprocal of the period, so f = 1/T. Therefore, the correctly modeled functions are f(x) = A * sin(2\(\pi\)/T * x) and f(x) = A * cos(2\(\pi\)/T * x), which correspond to options (a) and (b), respectively.