Precalculus activity

Question

Simple Harmonic Motion is a periodic motion that creates a sinusoidal (sine) wave. The equation for simple harmonic motion can be given as x(t) = Asin 𝜔t. The variables x(t) stands for displacement, A stands for amplitude, t stands for time.

 a. What could 𝜔 stand for? _______________ (Hint: think of the standard formula for a sine wave)

b. An object has a frequency of 5/2 oscillations per second, and an amplitude of 6 meters. Write an equation for the displacement of the object, using the given formula for x(t) above. NOTE: 𝜔 = 2𝜋𝑓, where f is the frequency. x(t) = _________

c. Recall that 𝑓 = 2𝜋 / 𝑇 . What does T stand for? __ ___. An object moves in simple harmonic motion described by x(t) = 3sin2t.

d. What are the Amplitude =_____, f = _________, and T= ________ d. Graph the equation given in part c. (Remember to be in radian mode)

Answer 1

a) ω is angular frequency, the number of radians traced out during one cycle or period.

b) Plug in: ω = 2π(5/2) radians per second and x(t) = 6 sin(5π t).

c) WRONG! ω = 2π / T and f = 1/T. Anyway, T is the period, number of seconds per cycle of 2π radians (and that's why frequency f is the simple inverse of T; f is cycles per second).

d) A is of course 3. 2π f = ω = 2, so f = 1/π. T = 1/f = π. [don't forget to provide a plot, with x in radians, not degrees!]