A linear spring is stretched length of 5.0 cm with mass m=.2kg. Calculate:

Question

a) Spring constant k, Angular frequency

b)Frequency f, and period T

Answer 1

Hello Ashtin,

To find the spring constant, set up the equation for equilibrium: kx = mg (you can do a diagram with mg pushing downward, kx pushing up)

m = 0.2 kg, g = 9.8, x = 0.05 m

solve for k: k = mg/x = 0.2*9.8/(0.05) = 39.2 N/n

For angular frequency: use the formula angular_frequency = ω = √(k/m) = √(39.2/0.2) = √196 = 14

so ω = 14 radians/second

For frequency: ω = 2π*f so f = ω/(2π) = 14/(2π) = 7/π = 2.23 Hz

For period: T = 1/f = 2π/ω= 2π/14 = π/7 = 0.45 seconds