Equation of Motion for Simple Harmonic Motion

In simple harmonic motion, the force that is creating the oscillation of the object obeys Hooke's Law. Suppose we examine the oscillation of a mass that is attached to a coil spring. The object will feel a force due to the coil spring and this force will be directly proportional to the displacement of the object. Suppose we wanted to determine the equation for the position of the object undergoing simple harmonic motion with respect to time. Does such a function exist? We see in our lecture that such a function does in fact exist but only when the square of the angular frequency is equal to the ratio of the spring stiffness constant to the mass of the object. From this result and from the fact that the angular frequency is equal to the product of the frequency and 2pi, we can derive an equation that will relate the frequency to the spring stiffness constant and the mass of the object. From this equation, we see that the amplitude does not affect the frequency of the oscillation, which means that if we increase or decrease the amplitude, the frequency will remain the same.

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