A 3.5 kg mass is attached to a spring with spring constant k= 55.0 N/m. The spri

Question

A 3.5 kg mass is attached to a spring with spring constant k= 55.0 N/m. The spring is compressed 12.0 cm and the released. A.) Write an equation of motion for the mass. B.) Find the kinetic and the potential energy when x= 4.0 cm. C.) What is the resonant frequency of this system? A 3.5 kg mass is attached to a spring with spring constant k= 55.0 N/m. The spring is compressed 12.0 cm and the released. A.) Write an equation of motion for the mass. B.) Find the kinetic and the potential energy when x= 4.0 cm. C.) What is the resonant frequency of this system?

Explanation / Answer

(A) x = - A cos(wt)

A = 12 cm and w = sqrt(k/m) = 3.96 rad/s

x = - (12 cm) cos(3.96 t)

(B) PE = k x^2 / 2 = 55 (0.04^2)/2 = 0.044 J ....Ans (Potential energy)

total energy = k A^2 /2 = 55(0.12^2)/2 = 0.396 J

KE = total energy - PE

= 0.352 J .......Ans

(f) w = 3.96 rad/s

f = w / 2pi = 0.63 Hz

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