After considering the motion of the system as whole, let us now consider the mass that...

 

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After considering the motion of the system as whole, let us now consider the mass that is attached to the oscillator. To do so, we must first recognize that we can describe position for simple harmonic motion in terms of a periodic function, namely the cosine function. Note that our use of a cosine function is based upon the initial conditions we selected. In other words, at t = 0, the spring is extended to a maximum, and the initial velocity is zero. For clarity, a general cosine graph is shown below. a Graphically, this can represent the position of the mass for a simple harmonic oscillator at some time t. Specifically, we get x = A cos(2xft) with x measured from the equilibrium position. Thus, for a harmonic oscillator with oscillations of amplitude A, we can use our knowledge of the attached mass and the spring constant to define the position as a function of time. For an oscillator with a spring constant of k= 8.00 N/m, amplitude of 1.00 m, and an attached mass of 0.600 kg, answer the following. If you extend the spring to a maximum and start your timer just as you release the mass, what will be the position of the mass after 15.0 seconds? (Enter your answer in m.) -0.905 X * Be aware that this problem has multiple components. If you want to determine the frequency of oscillation for a simple harmonic oscillator, which expressions can you use? Which expressions incorporate the terms given in the problem? Once you have calculated the frequency of oscillation, how can you relate that to a displacement or position? m After considering the motion of the system as whole, let us now consider the mass that is attached to the oscillator. To do so, we must first recognize that we can describe position for simple harmonic motion in terms of a periodic function, namely the cosine function. Note that our use of a cosine function is based upon the initial conditions we selected. In other words, at t = 0, the spring is extended to a maximum, and the initial velocity is zero. For clarity, a general cosine graph is shown below. a Graphically, this can represent the position of the mass for a simple harmonic oscillator at some time t. Specifically, we get x = A cos(2xft) with x measured from the equilibrium position. Thus, for a harmonic oscillator with oscillations of amplitude A, we can use our knowledge of the attached mass and the spring constant to define the position as a function of time. For an oscillator with a spring constant of k= 8.00 N/m, amplitude of 1.00 m, and an attached mass of 0.600 kg, answer the following. If you extend the spring to a maximum and start your timer just as you release the mass, what will be the position of the mass after 15.0 seconds? (Enter your answer in m.) -0.905 X * Be aware that this problem has multiple components. If you want to determine the frequency of oscillation for a simple harmonic oscillator, which expressions can you use? Which expressions incorporate the terms given in the problem? Once you have calculated the frequency of oscillation, how can you relate that to a displacement or position? m