Question
The position of an object connected to a spring varies with time according to the expression x = (7.1 cm) sin (2.1π t). Find
(a) the period of this motion (b) the frequency of the motion (c) the amplitude of the motion (d) the first time after t=0 that the object reaches the position x = 2.6 cm (Make sure your calculator is in radians mode)
(a) the period of this motion (b) the frequency of the motion (c) the amplitude of the motion (d) the first time after t=0 that the object reaches the position x = 2.6 cm (Make sure your calculator is in radians mode)
Answers
(a)
Compare
x = (7.1 cm) sin (2.1π t)
with
x=Asin(ωt)
Then
ω= 2.1π,
=> T=2π/ ω =
= 2 π/2.1π=0.7 rad/s
(b)
f=1/T=1.42 Hz
(c)
A=7.1 cm
(d)
x=Asin(ωt)
2.6 = 7.1 sin (2.1π t)
sin (2.1π t) =2.6/7.1=0.366
(2.1π t)=sin⁻¹0.366=0.375 rad
t=0.375/2.1π=0.0569 s.
Compare
x = (7.1 cm) sin (2.1π t)
with
x=Asin(ωt)
Then
ω= 2.1π,
=> T=2π/ ω =
= 2 π/2.1π=0.7 rad/s
(b)
f=1/T=1.42 Hz
(c)
A=7.1 cm
(d)
x=Asin(ωt)
2.6 = 7.1 sin (2.1π t)
sin (2.1π t) =2.6/7.1=0.366
(2.1π t)=sin⁻¹0.366=0.375 rad
t=0.375/2.1π=0.0569 s.