Please find the angular frequency, Thank you To understand the application of th
ID: 1513395 • Letter: P
Question
Please find the angular frequency,
Thank you
To understand the application of the general harmonic equation to finding the acceleration of a spring oscillator as a function of time. 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. (Figure 1) 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 of this problem is to determine the acceleration of the block a(t) as a function of time in terms of k, m. and x_init. It is known that a general solution for the position of a harmonic oscillator is x(t) = C cos (wt) + s sin (wt), where C, 5. and w are constants. (Figure 2) Combine Newton's 2nd law and Hooke's law for a spring to find the acceleration c of time. Express your answer in terms of k, m, and the coordinate of the block x(t). Using the fact that acceleration is the second deriva function of time. Express your answer in terms of w, t, and x(t). Find the angular frequency w. Express your answer in terms of k and m.Explanation / Answer
There is a simple straight forward formula for Angular freq in Simple Harmonic motion,
= sqrt(k/m)