Homework Help: physics mechanics

Posted by abu on Sunday, September 16, 2012 at 1:57pm.

A block weighing 17 N oscillates at one end of a vertical spring for which k = 120 N/m; the other end of the spring is attached to a ceiling. At a certain instant the spring is stretched 0.24 m beyond its relaxed length (the length when no object is attached) and the block has zero velocity. (a) What is the net force on the block at this instant? What are the (b) amplitude and (c) period of the resulting simple harmonic motion? (d) What is the maximum kinetic energy of the block as it oscillates?

physics mechanics - Elena, Sunday, September 16, 2012 at 5:28pm
If v=0, the block is at its extreme (end) position =>
x= x(max)=0.24 m = A (amplitude)

The equation of the oscillation is
x=Asinωt
v=Aωcosωt
a= - Aω²sinωt
F= - m Aω²sinωt = - mω²x = - kx,
x=A => F= kA = 120∙0.24= 28.8 N.
ω= √(k/m)= √(kg/W)=
=√(120∙9.8/17) = 8.32 rad/s
T=2π/ ω=2π/8.32=0.76 s.
KE(max) =PE(max) =kA²/2 = 120∙0.24²/2 = 3.456 J.

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