The period of motion of an object-spring system is T = 0.582 s when an object of mass m = 254 g is attached to the spring.(a) Find the frequency of motion in hertz. Hz(b) Find the force constant of the spring. N/m(c) If the total energy of the oscillating motion is 0.267 J, find the amplitude of the oscillations. m
Question
The period of motion of an object-spring system is T = 0.582 s when an object of mass m = 254 g is attached to the spring.(a) Find the frequency of motion in hertz. Hz(b) Find the force constant of the spring. N/m(c) If the total energy of the oscillating motion is 0.267 J, find the amplitude of the oscillations. m
Solution
(a) The frequency of motion in hertz can be found using the formula f = 1/T, where T is the period.
So, f = 1/0.582 = 1.7181 Hz.
(b) The force constant of the spring can be found using the formula k = 4π²m/T², where m is the mass and T is the period.
First, convert the mass from grams to kilograms: m = 254 g = 0.254 kg.
Then, k = 4π²(0.254 kg)/(0.582 s)² = 29.83 N/m.
(c) The amplitude of the oscillations can be found using the formula A = sqrt(2E/k), where E is the total energy and k is the force constant.
So, A = sqrt(2*0.267 J/29.83 N/m) = 0.047 m.
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