When a 5 kg mass is hung on a spring, it stretches by 4.0 cm. What is the spring

Question

When a 5 kg mass is hung on a spring, it stretches by 4.0 cm. What is the spring constant of the spring? If the system is set oscillating up and down by stretching it an additional 4.0 cm and releasing it, what is the period of oscillation? How fast is the mass moving as it passes back through the equilibrium point? How much potential energy is in the assembly when it is at its extreme displacement? If you want to make the system tear itself apart, what is the highest frequency (f not omega) that can be used as a driving force to cause the system to resonate?

Explanation / Answer

(A) Fnet = kx - m g = 0

k (0.04) = (5) (9.8)

k = 1225 N/m

(B) T = 2pi sqrt(m/k)

T = 2pi sqrt(5 / 1225) = 0.40 sec

(C) Vmax = A w

and w = 2pi / T = 15.65 rad/s

v = 0.04 x 15.65 = 0.626 m/s

(d) PE = k x^2 / 2 = 1225 x 0.04^2 /2

PE = 0.98 J

(e) f = 1/T = 2.5 Hz

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