For the simple harmonic motion described by the trigonometri

For the simple harmonic motion described by the trigonometric function, find the maximum displacement, the frequency, the value of d when t = 5, and the least positive value of t for which d = 0. Use a graphing utility to verify your results.

49 (a) Find the maximum displacement. (b) Find the frequency cycles per unit of time (c) Find the value of d when t = 5. d= (d) Find the least positive value of t for which d = 0

Solution

d = (1/49) sin(790*pi*t)

Std formula: y = Asin(Bx) where A is the amplitude and time period T = 2pi/B

So, a) maximum displacement = amplitude = 1/49

b) frequency , f = 1/T = B/2pi = 790pi/pi = 790 cylces per unit of time

c) d when t= 5

So, plug t=5 in d = (1/49) sin(790pi*5) = (1/49)(0) =0

d) d= 0

790pi = 0 or pi

least positive value : 790pi = pi

t= 1/790