A) An ideal spring hangs from the ceiling. A 1.85-kg mass is hung from the sprin

Question

A) An ideal spring hangs from the ceiling. A 1.85-kg mass is hung from the spring. After all vibrations have died away, the spring is found to have stretched 0.0315 m from its original length. The mass is then pushed up 0.0805 m from its equilibrium position and released. What is the kinetic energy of the mass at the instant it passes back through its equilibrium position?

B) A point rotates about the origin in the xy plane at a constant radius of 0.190 m and angular velocity of 7.67 rad/s. As you know, the projections of this point on the x- and y-axes undergo simple harmonic motion. What is the amplitude of this motion? _____m       What is its frequency? ______Hz      And its period? _____s

Explanation / Answer

spring constant = k = F/dx = (1.85*9.8)/0.0315 = 575.55 N/m

KE = 0.5*k*x^2 = 0.5*575.55*0.0805^2 = 1.865 J

B)

amplitude = radius = 0.19 m

frequency = f = w/2pi = 7.67/(2pi) = 1.22 Hz

T = 2pi/w = 0.82 s

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