Introduction Simple harmonic motion is a special type of periodic motion, such t

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Introduction Simple harmonic motion is a special type of periodic motion, such that an object will always follow the same path and at some point return to its initial position; it will take the same amount of time to make each round trip. Each round trip is called a cycle, and the amount of time it takes the object to complete one cycle is called the period, T. The reciprocal of the period is frequency f, the number of cycles per unit lime. TWo conditions must be met for an object to be in simple harmonic motion: 1. The restoring force, the force trying to return the object back to equilibrium, must be proporuonal to the displacement, but in the opposite direction. The farther away an object is displaced, the greater the restoring force. 2. The period must be independent of the initial displacement. No matter how far away an object is displaced, it always takes the same amount of time to make one cycle and return to that same point. One example of this motion is the simple pendulum; a mass m. connected to a rod or string of length 1. However, the displacement angle must be small, otherwise the period will become dependent on the angle. Another example is a mass m, connected to a spring with spring constant k. In each case, the mass is displaced from equilibrium and released. The mass then travels through the equilibrium point to an extremum, stops changes direction and travels back through equilibrium to the other extremum, stops and changes direction again to return to equilibrium and so on. Today's lab will focus on the second example which is governed by Hooke's Law, F = -kx. Thus, the restoring force F. is proportional to the displacement x, and the negative siRn represents the fact that the restoring force is opposite of the displacement. The conditions for simple harmonic motion are met. From Newtons 2nd Law, we can find that the acceleration is a. = -(k/m)x. Recall that the relationship hetween linear and rotational acceleration is a = romega2. Since x = r cos theta, and the motion is linear, x = r. in this case. Furthermore, omega = 2pif Thus, omega= and T = 2pi Food tor thought. Since k is a measure of spring stiffness, which spring in the collisions lab had a high, and which had a low, k? Goal To study simple harmonic motion In a mass spring system. What reasons would account for the %Difference? Speculate on sources of error.

Explanation / Answer

Error could be due to the enviromental factor such as air prassure or it may be due to the instrumental error, or may be due to person which is measuring the time period.

% diff =( 0.978-0.8251) / (0.978+0.8251) /2

           =16.95%

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