a 0.150 kg mass stretches a spring 20.0 cm when hung vertically. what is the spring constant? what is the period of the spring? make a graph with displacement, velocity, and acceleration as a function of time for one complete cycle.
F = -m g = -0.150 * 9.81 = -1.47 Newtons
F = -k x
1.47 = k (0.20)
k = 7.36 N/m
from that equilibrium point
F = -k x = m a = m d^2x/dt^2
-7.36 x = m d^2 x dt^2
if x = sin (2 pi t/T) [ assuming amplitude of 1 ]
velocity = dx/dt = (2 pi/T) cos (2 pi t/T)
acceleration = d^2x/dt^2 = -(2 pi /T)^2 sin (2 pi t/T) = - (2 pi /T)^2 x
thus
-7.36 x = -0.15 (2 pi / T)^2 x
(2 pi /T)^2 = 7.36 / .15 = 49.1
2 pi /T = 7.00
T = 2 pi / 7 = 0.897 second period
go back and get velocity and acceleration from formulas above assuming amplitude of 1 since they did not tell you what it was to be