Question

A spring is hing from a ceil ing, and an object attached to its ower end stretches the spring tbr a distauce d . 5.00 cm from its unstretched pusition wheu the system in in equilibrium as in Figure P13.5. If the spring constant is The period of motion of an object-spring system is T= 0.528 s when an object of mass m- 238 g is attached to the spring. Find (a) the frequency of motion in hertz and (b) the force constant of the spring. (c) If the total energy of the oscillating motion is 0.234 J. find the amplitude of the oscillations. determine the mass Figure P13.5 of the object.

Answer 1

From Hooke's lawF = kxmg = kx m = kx/g = 47.5 times 5 times 10^-2 m/9.8 = 2.375/9.8 = 2.375/9.8 = 0.242 kg a) T = 0.528 sec m = 238 g = 0.233 kg f = 1/4 = 1/0.528 = 1.893 HZ b) w = squareroot k/m k = w^2 m = (2 pi/T)^2 times m = (2 pi/0.525)^2 times 0.238 = 33.668 N/m c) E = 1/2 KA^2 0.234 = 1/2 (33.668) A^2 = 16.834 A^2 A^2 = 0.234/16.334 rightwardsdoublearrow 0.11790 m = A A = 0.11790 m