The position of an object connected to a spring varies with time according to the expression x (5.2 cm) sin (8.0 pt). Find (a) the period of this motion, (b) the frequency of the motion, (c) the amplitude of the motion, and (d) the fi rst time after t 0 that the object reaches the position x 2.6 cm.

A. Period (T) = 0.25rad/s

B. Frequency (f) = 4.0hz

C. Amplitude (A) = 5.2cm

D. Time (t) = 0.6256secs

Explanation:

A. Firstly, we Compare the equation

x = (5.2 cm) sin (8.0π t)

with

x=Asin (ωt) (General equation)

Then

ω = 2πt

=> T=2π / ω =

= 2 π/8.0π=0.25rad/s

B. frequency (f) = 1/T

= 1/0.25

= 4.0hz

C. A = 5.2 cm by comparison with the general equation.

D. x = Asin (ωt)

2.6 = 5.2sin (8.0π t)

sin (8.0π t) =

2.6/5.1 = 0.5098

(8.0π t) = sin⁻¹0.5098 = 30.650

t = 30.650/8.0π

t = 0.6256secs