Question
What mass on a spring with a spring constant of 120 N/m will oscillate with a period of 1.0 s?
Answers
Damon
F = -k x = m a
if x = a sin 2 pi f t
v = 2 pi f a cos 2 pi f t
a = - (2 pi f)^2 a sin 2 pi f t
so
a= -(2 pi f)^2 x
then
-k x = -m (2 pi f)^2 x
(2 pi f)^2 = k/m
here T = 1/f = 1 so f = 1/1 = 1 Hz
(2 pi)^2 = 120/m
m = 30/( pi^2) = 3.04 kg
if x = a sin 2 pi f t
v = 2 pi f a cos 2 pi f t
a = - (2 pi f)^2 a sin 2 pi f t
so
a= -(2 pi f)^2 x
then
-k x = -m (2 pi f)^2 x
(2 pi f)^2 = k/m
here T = 1/f = 1 so f = 1/1 = 1 Hz
(2 pi)^2 = 120/m
m = 30/( pi^2) = 3.04 kg