One end of a spring with spring constant k is attached to the wall. The other end is attached to a block of mass m. The block rests on a frictionless horizontal surface. The equilibrium position of the left side of the block is defined to be x = 0. The length of the relaxed spring is L.
http://session.masteringphysics.com/problemAsset/1010960/28/MHM_de_0_a.jpg
The block is slowly pulled from its equilibrium position to some position x_init > 0 along the x axis. At time t=0 , the block is released with zero initial velocity.
The goal is to determine the position of the block x(t) as a function of time in terms of omega and x_init.
It is known that a general solution for the displacement from equilibrium of a harmonic oscillator is
x(t) = C*cos(omega*t) S*sin(omega*t)
where C, S, and omega are constants.
http://session.masteringphysics.com/problemAsset/1010960/28/MHM_de_0_b.jpg
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Find the value of S using the given condition that the initial velocity of the block is zero: v(0)=0.
A: x_init*tan(omega*t)
B: x_init*omega
C: x_init
D: 0
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Please pick from A-D and explain your reasoning
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