Question
A 326 g object is attached to a spring and oscillates with a period of 0.25 s. The total energy in this system is 5.83 J. What is the amplitude of the motion?
Answers
drwls
The total energy of the system is the spring potential energy at maximum displacement, which is the Amplitude, X
(1/2) k X^2 = 5.83 J
You need the spring constant, k, to compute X. Get it from the period, P = 0.25 s
P = 2 pi sqrt(M/k) = 0.25 s
sqrt(M/k) = 0.25/(2 pi) = 0.0398 s
M/k = 1.583*10^-3 s^2
k = 205.9 N/m
Now solve the first equation for X
(1/2) k X^2 = 5.83 J
You need the spring constant, k, to compute X. Get it from the period, P = 0.25 s
P = 2 pi sqrt(M/k) = 0.25 s
sqrt(M/k) = 0.25/(2 pi) = 0.0398 s
M/k = 1.583*10^-3 s^2
k = 205.9 N/m
Now solve the first equation for X