Question

A 1.25 kg mass oscillates on a spring with a period of 5.00 s. During oscillation the minimum length of the spring is 4.00 cm and the maximum length of the spring is 9.50 cm. What is the total energy of this system?

Answer 1

we first need to find the oscillation freqency = f = (k/m)^1/2 / 2

time period T = = 1/f

f=1/T

given, time period = 5s

f = 1/5 = 0.2

0.2 = (k/m)^1/2 / 2

k/m = (0.4)²

k = m* (0.4)² =

= 1.25*1.579

k = 1.9739

when the spring is fully stretched, the total energy =kinetic energy = 1/2mv² where v is the velocity of mass

when the spring is fully compresses, the total energy = potential energy = 1/2 kx² where x is the displacement of mass

we see that the spring's max length is 9.50cm

minimum length = 4cm

so total displacement = 5.5cm = 0.055m

max potential enegy = energy of system = 1/2kx²

                                                          = 0.5*1.9739*(0.055)²

                                                           E =0.003 jouls--------------------answer