Answer to Question #68089 in Mechanics | Relativity for Hello dear

Question

The scale of a spring balance reading from 0 to 50 lb is 4 inch long.A pakage suspended from the balance is found to oacillate vertically eith a frequency of 2.0 Hz.how much does the pakage weigh?

Answer 1

Newton's second law:
mg= kx (1), where k is the coefficient of elasticity, m=50lb=22.68 kg, g=9.8 N/kg, x=4inch=0.1016 m
Of (1) k= mg/x (2)
Of (2) k=2187.64 N/m
The oscillation frequency:
1/f= 2π sqrt(m/k) (3)
Of (3) m= k/4π2f2 (4), where k=2187.64 N/m, f=2 Hz
Of (4) m=13.87 kg
Answer:
13.87 kg or 30.58 lb