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?

Answer 1

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