The period, T, of the motion of the particle oscillating on the end of an elastic string is
inversely proportional to the square root of the stiffness of the string, k. When an object of
mass 2 kg is suspended from a string with the stiffness of 10 N/m, it oscillates with the period
of 2pi/7 seconds. Find:

Question

The period, T, of the motion of the particle oscillating on the end of an elastic string is
inversely proportional to the square root of the stiffness of the string, k. When an object of
mass 2 kg is suspended from a string with the stiffness of 10 N/m, it oscillates with the period
of 2pi/7 seconds. Find:

anonymous · Answer

a. the period when the same object oscillates on the end of the elastic string with the
stiffness of 25 N/m
b. the stiffness of the string, if the time needed for one oscillation is 32pi/7

stamp · Answer

$$t(k)=1/k^2$$$$a.\ t(25)=1/25^2=1/525$$$$b.\ 32\pi/7=1/k^2$$$$k^2=7/(32\pi)$$$$k=\sqrt{7/(32\pi)}$$