Simple Harmonic Motion

The second way that will we measure the frequency is

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Unformatted text preview: sure the frequency is be using the spring constant. We know that the frequency is related to the spring constant as 1 2 (68) However for this experiment, we have two spring and thus two spring constants. Thus we must write the total spring constant k (See Figure 11) as (69) Therefore equation (68) becomes 1 2 (70) 12 4.2 Simple Pendulum For the second part of this experiment, you will measure the period of a simple pendulum. You will then use the period to calculate the frequency of the simple pendulum and compare that value to the theoretical value predicted using the small angle approximation. We know that the frequency is related to the period as Figure 11 Diagram of mass attached to two strings. This is similar to the experiment that you will be performing. ingsandaMass.html 1 (71) You can see that the frequency is simply just the inverse of the period and vice versa. Once you measure the period you will use the small angle approximation of the simple pendulum 1 2 (72) Once you calculate the frequency, you will then find the % Difference of the frequency predicted by equation (65) and the one measured using equation (71). Now that you have the theoretical value for the frequency, you will notice that it involves gravity. Thus we can measure gravity by knowing the frequency and the length of the pendulum. Thus we can find gravity using 2 (73) For the final part of the calculation of the simple pendulum you will find the acceleration of gravity using the frequency that you measured and putting this into equation (73). 4.3 Physical Pendulum The final thing that you will do in the lab, is measure the frequency of a physical pendulum so the first measure the length of the rod L, the rod mass MR, and the mass of the brass (bob) MM. We will start with the predicted frequency of a physical pendulum which is given by 1 2 (74) where M is the total mass of the pendulum, h is the distance from the pivot point to the center-of-mass of the pendulum, and I is the rotational inertia of a thin rod about its end. From Table 1 of the angular motion lab, we know tha...
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