A 3-Kg object stretches a spring 16 cm when hangs vertically in equilibrium. The

Question

A 3-Kg object stretches a spring 16 cm when hangs vertically in equilibrium. The spring is then streched from its equilibrium position and the object is released. (a) Find the frequency of the motion (b) Find the frequency if the 3-Kg object is replaced with a 6-Kg object. (c) With the 3-Kg object hanging, the spring is streched 5 cm from its 'new' equilibrium position and the object is released Find the total energy of the spring when the mass is at its maximum displacement. (d) Find the potential energy of the spring when the mass is at its maximum displacement. (Note-help: to find the potential energy subtract the gravitational energy from the total energy.

Explanation / Answer

Here ,

a) m = 3 Kg

x0 = 0.16 m

let the spring constant is k

as m * g = k * x0

3 * 9.8 = k * 0.16

solving for k

k = 183.8 N/m

frequency of motion = 1/(2pi) * sqrt(183.8/3)

frequency of motion = 1.25 Hz

b)

frequency of motion = 1/(2pi) * sqrt(183.8/6)

frequency of motion = 0.881 Hz

c)

Total energy = 0.50 * k * A^2

Total energy = 0.50 * 183.8 * 0.05^2

Total energy = 0.23 J

d)

at the maximum displacement

potential energy = 0.23 - 3 * 9.8 * 0.05

potential energy = -1.24 J

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